Pam-4 dfe architectures with symbol-transition dependent dfe tap values

ABSTRACT

Decision feedback equalization (DFE) is used to help reduce inter-symbol interference (ISI) from a data signal received via a band-limited (or otherwise non-ideal) channel. A first PAM-4 DFE architecture has low latency from the output of the samplers to the application of the first DFE tap feedback to the input signal. This is accomplished by not decoding the sampler outputs in order to generate the feedback signal for the first DFE tap. Rather, weighted versions of the raw sampler outputs are applied directly to the input signal without further analog or digital processing. Additional PAM-4 DFE architectures use the current symbol in addition to previous symbol(s) to determine the DFE feedback signal. Another architecture transmits PAM-4 signaling using non-uniform pre-emphasis. The non-uniform pre-emphasis allows a speculative DFE receiver to resolve the transmitted PAM-4 signals with fewer comparators/samplers.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram illustrating a communication system with decisionfeedback equalization (DFE).

FIG. 2 is a diagram illustrating a memory system.

FIG. 3A illustrates a non-speculative DFE four-level pulse amplitudemodulation (PAM-4) receiver with analog feed-forward equalization (FFE).

FIG. 3B illustrates a non-speculative DFE two-level pulse amplitudemodulation (PAM-2) receiver with analog FFE.

FIG. 4A illustrates a non-speculative DFE PAM-4 receiver with acombination receive FFE and first tap DFE loop.

FIG. 4B illustrates a non-speculative DFE PAM-2 receiver with acombination receive FFE and first tap DFE loop.

FIG. 5 illustrates a non-speculative DFE receiver with analog FFE andhigher order DFE taps.

FIG. 6 illustrates a non-speculative DFE receiver with receive FFE andhigher order DFE taps.

FIG. 7 illustrates a non-speculative DFE receiver with low-latency DFEtap feedback.

FIG. 8 illustrates a PAM-4 receiver with low-latency DFE feedback.

FIG. 9 illustrates a PAM-4 receiver with DFE feedback.

FIG. 10 illustrates a receiver with DFE feedback.

FIG. 11 illustrates a receiver with higher order DFE feedback.

FIG. 12 illustrates a communication system with non-uniform transmitequalization and speculative DFE.

FIGS. 13A-13C illustrate an examples of non-uniform transmitequalization.

FIG. 14A illustrates PAM-4 data eyes for non-uniformly equalizedtransitions from positively signed previous symbols.

FIG. 14B illustrates PAM-4 data eyes for non-uniformly equalizedtransitions from negatively signed previous symbols.

FIG. 15 illustrates a PAM-4 speculative DFE receiver with fivecomparators.

FIG. 16 illustrates a PAM-4 speculative DFE receiver with second tapfeedback.

FIG. 17 illustrates a PAM-4 speculative DFE receiver having second tapfeedback without subtraction.

FIG. 18 is a flowchart illustrating a non-speculative decoder freemethod of decision feedback equalization.

FIGS. 19A-19B are a flowchart illustrating a non-speculative method ofdecision feedback equalization.

FIG. 20 is a flowchart illustrating non-speculative DFE using an analogFFE.

FIG. 21 is a flowchart illustrating non-speculative DFE using acombination receive FFE and first tap DFE loop.

FIG. 22 illustrates a communication system with an analog-to-digitalconverter (ADC) based receiver.

FIG. 23 illustrates a receiver with higher order DFE feedback in thedigital domain.

FIG. 24 is a flowchart illustrating a method of equalizing a datasignal.

FIG. 25 is a block diagram of a computer system.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Decision feedback equalization (DFE) is used to help reduce inter-symbolinterference (ISI) from a data signal received via a band-limited (orotherwise non-ideal) channel. In an embodiment, a PAM-4 DFE architecturehas low latency from the output of the samplers to the application ofthe first DFE tap feedback to the input signal. This is accomplished bynot decoding the sampler outputs in order to generate the feedbacksignal for the first DFE tap. Rather, weighted versions of the rawsampler outputs are applied directly to the input signal without furtheranalog or digital processing.

In other embodiments, additional PAM-4 DFE architectures use the currentsymbol in addition to previous symbol(s) to determine the DFE feedbacksignal. For example, an analog sample and hold circuit is used tocapture the voltage level of a symbol while it is the current symbol.This captured voltage is held until the next symbol period, weighted,and then analog added to a weighted version of the current inputvoltage. This implements an analog feed-forward equalizer that utilizesthe current symbol. In another example, a weighted version of thecurrent input voltage is added to a first DFE tap voltage. The sum ofthese inputs is sampled to produce the first DFE tap voltage for thenext symbol period.

A finite impulse response (FIR) filter is used to provide non-uniformpre-emphasis to a PAM-4 output signal. The non-uniform pre-emphasisvalues are selected such that, after passing through the channel,several of the received voltage levels have approximately the samevalues. In other words, the non-uniform pre-emphasis is combined withthe ISI caused by the channel to allow certain transitions to be sampledusing the same reference voltages rather than different referencevoltages. This allows the use of fewer comparators (e.g., five insteadof twelve) to speculatively sample the received PAM-4 signal.

FIG. 1 is a diagram illustrating a communication system with decisionfeedback equalization (DFE). Communication system 100 comprises adriving integrated circuit, a receiving integrated circuit, andinterconnect between them. The driving integrated circuit includestransmitter circuit 110 (a.k.a., a driver). Transmitter circuit 110 mayuse finite impulse response (FIR) based equalization. Transmittercircuit 110 may include tap drivers 113. Tap drivers 113 may include oneor more pre-tap FFE drivers, one or more post-tap FFE drivers, and amain tap driver.

The receiver integrated circuit includes receiver circuit 150. Theinterconnect between the driving integrated circuit and the receivingintegrated circuit comprises interconnect system 140. Interconnectsystem 140 would typically comprise a printed circuit (PC) board,connector, cable, flex circuit, other substrate, and/or a combination ofthese. Interconnect system 140 may be and/or include one or moretransmission lines.

Receiver circuit 150 would typically be part of an integrated circuitthat is receiving the signal sent by the driving integrated circuit. Itshould be understood that termination (not shown in FIG. 1) can be partof the integrated circuit or interconnect system 140. It should also beunderstood that although system 100 is illustrated as transmitting asingle-ended signal, the signals sent by the driving integrated circuitof system 100 may represent one of a pair of differential signals or oneof a collection of signals sending multi-wire-coded data.

In FIG. 1, the output of transmitter circuit 110 is connected to a firstend of interconnect system 140. The second end of interconnect system140 is connected to the input of receiver 150. In an embodiment,transmitter circuit 110 may be configured to drive PAM-4 signalinglevels. In another embodiment, transmitter circuit 110 may be configuredto drive PAM-2 (non-return to zero—NRZ) signaling levels.

In an embodiment receiver 150 uses a PAM-4 DFE architecture that has lowlatency from the output of the samplers to the application of the firstDFE tap feedback to the input signal. Appropriately weighted versions ofthe raw sampler outputs are applied directly to the input signal withoutfurther analog or digital processing. By applying the weighted versionsof the raw sampler outputs directly to the input signal, the latencyassociated with processing the sampler outputs into a single DFE tapvalue is reduced.

In an embodiment, receiver 150 uses a DFE architecture that uses thecurrent input voltage (symbol) received via interconnect system 140 asan input to help determine the DFE feedback signal. Receiver 150 addsthe current input symbol to the higher (i.e., greater than 1) DFEfeedback taps (if any) to produce a first input voltage. Receiver 150may use an analog sample and hold circuit to capture this first inputvoltage during the current symbol period. Receiver 150 holds thecaptured first input voltage during the next symbol period. Receiver 150weights the captured first input voltage. Receiver 150 analog adds thisweighted version to an analog weighted version of the current inputvoltage (i.e., the next symbol). Receiver 150 therefore implements ananalog feed-forward equalizer that utilizes the current symbol.

In an embodiment, receiver 150 adds the current input symbol to thehigher (i.e., greater than 1) DFE feedback taps (if any) to produce afirst input voltage. Receiver 150 analog weights this first inputvoltage to produce a weighted version of the first input voltage.Receiver 150 analog adds this weighted version of the first inputvoltage to a first DFE tap voltage produced from the sampled (digital)version of the previous symbol. The sum of these two inputs is sampledby receiver 150 to produce the first DFE tap voltage for the next (i.e.,subsequent) symbol period.

In an embodiment, receiver 150 is a speculative DFE receiver.Transmitter circuit 110 uses a finite impulse response (FIR) filter toapply non-uniform pre-emphasis to a PAM-4 output signal. The non-uniformpre-emphasis applied by transmitter circuit 110 is selected such that,after passing through interconnect system 140, several of the receivedPAM-4 voltage levels have effectively the same values. The non-uniformpre-emphasis applied by transmitter circuit 110 combined with the ISIcaused by interconnect system 140 allow certain PAM-4 transitions sentby transmitter circuit 110 to be accurately sampled by speculative DFEreceiver 150 using five comparators.

PAM-4 voltage levels may be assigned the values −3, −1, +1, and +3.These values are assumed for the discussion herein. In addition, for thediscussion herein, the letter ‘a’ is used to denote these symbol valuesin digital/integer form (i.e., −3, −1, +1, and +3) and the letter ‘v’ todenote these symbol values and other voltages in their analog form(e.g., −30 mV, −10 mV, +10 mV, +30 mV).

A desirable non-speculative DFE receiver (e.g., receiver 150) wouldimplement the first DFE tap to be based on the current symbol accordingto the following Equation 1:

dfe ₁=−0.5α₁(a ⁻¹ −a ₀)  EQN. 1

where dfe₁ is the desirable DFE tap value for the first post-cursor DFEtap; a⁻¹ is the previous symbol; a₀ is the current symbol; and α₁ is theamount of ISI associated with a transition between two adjacent, withrespect to signal/voltage, PAM-4 levels (e.g., from +1 to −1, −3 to −1,etc.) for the first post-cursor ISI. Thus, a desirable non-speculativeDFE receiver (e.g., receiver 150) would implement the first DFE tapaccording to Table 1.

TABLE 1 Previous Current Symbol Symbol DFE Tap a⁻¹ a₀ (a⁻¹ − a₀)−0.5(a⁻¹ − a₀) Value +3 +3 0 0 0 +3 +1 +2 −1 −1α +3 −1 +4 −2 −2α +3 −3+6 −3 −3α +1 +3 −2 +1  +α +1 +1 0 0 0 +1 −1 +2 −1  −α +1 −3 +4 −2 −2α −1+3 −4 +2 +2α −1 +1 −2 +1  +α −1 −1 0 0 0 −1 −3 +2 −1  −α −3 +3 −6 +3 +3α−3 +1 −4 +2 +2α −3 −1 −2 +1  +α −3 −3 0 0 0

For the second and higher DFE tap values, (e.g., DFE tap # n, where n=2,3, 4 . . . ), it can be shown that the amount of ISI a previous symbola_(−n) has on a current symbol a₀ depends on the trajectory between thetwo adjacent symbols a_(−n) and a_(−(n-1)). Therefore, desired valuesfor higher DFE taps can be expressed according to Equation 2:

dfe _(n)=−½(a _(−n) −a _(−(n-1)))α_(n)=−0.5(a _(−n) −a_(−(n-1)))α_(n)  EQN. 2

where dfe_(n) is the desirable DFE tap value for the n^(th) post-cursorDFE tap; a_(−(n-1)) is the symbol immediately previous to the n^(th)symbol; a_(−n) is the current symbol; and α_(n) is the amount of ISIassociated with a transition magnitude of a single PAM-4 level (e.g.,from +1 to −1, −3 to −1, etc.) for the n^(th) post-cursor ISI.

In accordance with Equation 1 and Equation 2, the Equations in Table 2generalize the desirable DFE tap values for all taps. In Table 2, v_(m)is the received voltage; m is the time index; h_(o), h₁, h₂, etc. arethe discrete-time voltage values of the channel (e.g., interconnectsystem 140) single-bit response; and a_(m) is the m^(th) transmittedsymbol.

TABLE 2 v_(m) = a_(m)h₀ + 0.5(a_(m−1) − a_(m))h₁ + 0.5(a_(m−2) −a_(m−1))h₂ + ...  dfe₁ = −0.5(a_(m−1) − a_(m))α₁ dfe₂ = −0.5(a_(m−2) −a_(m−1))α₂ dfe₃ = −0.5(a_(m−3) − a_(m−2))α₃ etc. sampler input =a_(m)h₀ + 0.5(a_(m−1) − a_(m))(h₁ − α₁) + 0.5(a_(m−2) − a_(m−1))(h₂ −α₂) + ...  where a_(i) = {+3, +1, −1, −3}

It should be understood that as used herein, h is the single-bitresponse (SBR). In other words, when plotting the single-bit responsesuch that the Y axis is in units of volts and x is in units of time, thesingle-bit response is obtained by convolving channel impulse response(e.g., impulse response of interconnect 140) with an ideal bit (i.e. asquare shaped signal). To find the effect of ISI on each symbol (bit)the single-bit response needs to be used. When h is used with asubscript (i.e. h₀, h₁, h₂ . . . h_(m), refer to samples of continuous awaveform h, acquired at uniformly spaced time instances, where each twoadjacent sampling intervals are apart by 1 UI—unit interval—equal to1/(data rate). The point that h has its maximum amplitude may bereferred to as cursor, or h₀. The subscript zero (0) refers to the factthat cursor is used as the time reference. The sample coming 1 UI after(right side on a time axis running left to right) of h₀ is called firstpost-cursor, or h₁. The sample that precedes (left side) h₀ is calledfirst pre-cursor, or h⁻¹. To illustrate how to calculate the effect ofISI on the current bit voltage amplitude, v₀, assume a simplifiedchannel that only has 1 pre-cursor, and 1 post-cursor. In this case, forexample:

v ₀=(current symbol)×h ₀+(next symbol)×h ⁻¹+(previous symbol)×h ₁

Note that the symbol in NRZ (i.e., PAM-2) signaling can have a value ofeither −1 or +1. For PAM-4 signaling the symbol can have a value of −1,−⅓, +⅓ or +1.

FIG. 2 is a block diagram illustrating a memory system. In FIG. 2,memory system 200 comprises memory controller 210 and memory 220. Memorycontroller 210 includes drivers 213 and receivers 214. Memory controller210 also includes N number of signal ports Q[1:N] that may be driven byone or more of drivers 213 and may receive signals to be sampled by oneor more of receivers 214. Memory 220 includes drivers 223 and receivers224. Memory 220 also includes N number of signal ports Q[1:N] that maybe driven by one or more of drivers 223 and may receive signals to besampled by one or more of receivers 224. Signal ports Q[1:N] of memorycontroller 210 are operatively coupled to ports Q[1:N] of memory 220,respectively. Receivers 224 of memory 220 may receive one or more of theQ[1:N] signals from memory controller 210. Receivers 214 of memorycontroller 210 may receive one or more of the Q[1:N] signals from memory220.

One or more of drivers 213 when configured and coupled with acorresponding one or more receivers 224 may form a PAM-2 signalingsystem or a PAM-4 signaling system. Thus, one or more of drivers 213 ofmemory controller 210 may correspond to transmitter circuit 110,discussed previously, or correspond to a transmitter circuit discussedherein subsequently. The one or more of drivers 213 of memory controller210 may apply pre-emphasis to drive a (two- or four-level) signal. Oneor more of receivers 214 of memory controller 210 may correspond toreceiver 150, discussed previously, or correspond to a receiver circuitdiscussed herein subsequently. The one or more of receivers 214 ofmemory controller 210 may use a DFE architecture that uses the currentinput voltage (symbol) received via from memory 220 as an input to helpdetermine a DFE feedback signal.

One or more of drivers 223 when configured and coupled with acorresponding one or more receivers 214 may form a PAM-2 signalingsystem or a PAM-4 signaling system. Thus, one or more of drivers 223 ofmemory 220 may correspond to transmitter circuit 110, discussedpreviously, or correspond to a transmitter circuit discussed hereinsubsequently. The one or more of drivers 223 of memory 220 may applypre-emphasis to drive a (two- or four-level) signal. One or more ofreceivers 224 of memory 220 may correspond to receiver 150, discussedpreviously, or correspond to a receiver circuit discussed hereinsubsequently. The one or more of receivers 224 of memory 220 may use aDFE architecture that uses the current input voltage (symbol) receivedfrom memory controller 210 as an input to help determine a DFE feedbacksignal.

Memory controller 210 and memory 220 are integrated circuit typedevices, such as one commonly referred to as a “chip”. A memorycontroller, such as memory controller 210, manages the flow of datagoing to and from memory devices, such as memory 220. For example, amemory controller may be a northbridge chip, an application specificintegrated circuit (ASIC) device, a graphics processor unit (GPU), asystem-on-chip (SoC) or an integrated circuit device that includes manycircuit blocks such as ones selected from graphics cores, processorcores, and MPEG encoder/decoders, etc. Memory 220 can include a dynamicrandom access memory (DRAM) core or other type of memory cores, forexample, static random access memory (SRAM) cores, or non-volatilememory cores such as flash. In addition, although the embodimentspresented herein describe memory controller and components, the instantapparatus and methods may also apply to chip interfaces that effectuatesignaling between separate integrated circuit devices.

It should be understood that signal ports Q[1:N] of both memorycontroller 210 and memory 220 may correspond to any input or output pins(or balls) of memory controller 210 or memory 220 that transmitinformation between memory controller 210 and memory 220. For example,signal ports Q[1:N] can correspond to bidirectional data pins (or padmeans) used to communicate read and write data between memory controller210 and memory 220. The data pins may also be referred to as “DQ” pins.Thus, for a memory 220 that reads and writes data up to 16 bits at atime, signal ports Q[1:N] can be seen as corresponding to pins DQ[0:15].In another example, signal ports Q[1:N] can correspond to one or moreunidirectional command/address (C/A) bus. Signal ports Q[1:N] cancorrespond to one or more unidirectional control pins. Thus, signalports Q[1:N] on memory controller 210 and memory 220 may correspond topins such as CS (chip select), a command interface that includes timingcontrol strobes such as RAS and CAS, address pins A[0:P] (i.e., addresspins carrying address bits), DQ[0:X] (i.e., data pins carrying databits), etc., and other pins in past, present, or future devices.

FIG. 3A illustrates a non-speculative DFE four-level pulse amplitudemodulation (PAM-4) receiver with analog feed-forward equalization (FFE).Receiver 300, illustrated in FIG. 3A, may correspond to one or more ofreceiver 150, receivers 214, and/or receivers 224. In an embodiment,receiver 300 may be configured to implement DFE tap values as describedherein. In particular, receiver 300 may implement DFE tap values asgiven in one or more of Equation 1, Equation 2, Table 1, and/or Table 2.

Receiver 300 comprises analog summer 311, sample-and-hold (S/H) circuit340, weighted buffer 341, weighted buffer 342, and PAM-4 sampler 320.PAM-4 sampler 320 includes sampler 321, sampler 322, and sampler 323.Samplers 321-323 output digital signals that can be interpreted to beeither +1 or −1. Weighted buffers 341-342 receive and output analogsignals that do not need interpretation.

An input signal (IN) is operatively coupled to the input of S/H 340 andthe input of weighted buffer 342. Input signal (IN) may be receivedfrom, for example, interconnect system 140. Weighted buffer 342 outputsthe analog voltage at the input to weighted buffer 342 multiplied by thefactor K0. In an embodiment, K0=1+0.5α₁, where α₁ is may be adapted orselected to remove the first post-cursor ISI component. When α₁ isdynamically adapted, it should be understood that K0 may be variableduring an adaptation (i.e., training) period, but is typically constantduring normal operation.

Sample-and-hold 340 samples and holds according to a timing reference(CK) that is synchronized to symbol periods such that S/H 340 will takean analog sample of the voltage on the input to S/H 340 at the same timePAM-4 sampler 320 is controlled to sample. This analog sample is held atthe output of S/H 340 until a new analog sample is taken during the nextsymbol period.

The output of S/H 340 is input to weighted buffer 341. Weighted buffer341 outputs the analog voltage at the input to weighted buffer 341multiplied by the factor K1. In an embodiment, K1=−0.5α₁. Similar to K0,it should be understood that K1 may be variable during an adaptation(i.e., training) period, but is typically constant during normaloperation.

The outputs of weighted buffer 341 and weighted buffer 342 are input toanalog summer 311. The output of analog summer 311 is input to PAM-4sampler 320. The output of analog summer 311 is input to thenon-inverting inputs of samplers 321-323. The inverting input of sampler321 receives reference voltage Vref1. The inverting input of sampler 322receives reference voltage Vref2. The inverting input of sampler 323receives reference voltage Vref3. Reference voltages Vref1, Vref2, andVref3 are typically selected to be between PAM-4 voltage levels. Forexample, if the four PAM-4 levels are −3V, −1V, +1V, and +3V, Vref1 maybe selected to be −2V, Vref2=0V, and Vref3=+2V.

Samplers 321-323 each receive a timing reference CK. CK determines thetiming that samplers 321-323 compare inputs (i.e., output of summer 311)to their respective reference voltage (e.g., Vref1, etc.) to producetheir respective digital output signal.

The voltage at the input of PAM-4 sampler 320 can be expressed by theEquations in Table 3. In Table 3, v_(m) is the received voltage; m isthe time index h_(o), h₁, h₂, etc. are the discrete-time voltage valuesof the channel (e.g., interconnect system 140) single-bit response;a_(m) is the m^(th) transmitted symbol; and β is the ISI at the outputof S/H 340.

TABLE 3 define Δ= 0.5(a_(m−1) − a_(m))  v_(m) = a_(m)h₀ + Δh₁ v_(m−1) =a_(m−1)h₀ + Δβ sampler input: v_(m) − 0.5(v_(m−1) − v_(m))α₁ samplerinput: a_(m)h₀ + Δ(h₁ − h₀α₁) + 0.5Δα₁(h₁ − β) (during adaptation)sampler input: a_(m)h₀ + 0.5Δα₁(h₁ − β) (steady state as α₁ → h₁/h₀)

FIG. 3B illustrates a non-speculative DFE two-level pulse amplitudemodulation (PAM-2) receiver with analog FFE. Receiver 302 illustrated inFIG. 3B may correspond to one or more of receiver 150, receivers 214,and/or receivers 224. In an embodiment, receiver 302 may be configuredto implement DFE tap values as described herein. In particular, receiver302 may implement DFE tap values as given in one or more of Equation 1,Equation 2, Table 1, and/or Table 2.

Receiver 302 comprises analog summer 311, sample-and-hold (S/H) circuit340, weighted buffer 341, weighted buffer 342, and sampler 322. Thus, itshould be evident from FIG. 3B that receiver 302 is similar to receiver300 but without sampler 321 and sampler 323. Also, receiver 302 has theinverting input of sampler 322 coupled to Vref4. In an embodiment,Vref4=Vref2=0V.

FIG. 4A illustrates a non-speculative DFE PAM-4 receiver with acombination receive FFE and first tap DFE loop. Receiver 400,illustrated in FIG. 4A, may correspond to one or more of receiver 150,receivers 214, and/or receivers 224. In an embodiment, receiver 400 maybe configured to implement DFE tap values as described herein. Inparticular, receiver 400 may implement DFE tap values as given in one ormore of Equation 1, Equation 2, Table 1, and/or Table 2.

Receiver 400 comprises analog summer 411, weighted buffer 441, weightedbuffer 435, weighted buffer 436, weighted buffer 437, and PAM-4 sampler420. PAM-4 sampler 420 includes sampler 421, sampler 422, and sampler423. Samplers 421-423 output digital signals that can be interpreted tobe either +1 or −1. Weighted buffer 441 receives an analog signal thatdoes not need interpretation.

An input signal (IN) is operatively coupled to the input to weightedbuffer 441. Input signal (IN) may be received from, for example,interconnect system 140. Weighted buffer 441 outputs the analog voltageat the input to weighted buffer 441 multiplied by the factor K0. In anembodiment, K0=1+0.5α₁, where α₁ is adapted or selected to remove thefirst post-cursor ISI component. When α₁ is dynamically adapted, itshould be understood that K0 may be variable during an adaptation (i.e.,training) period, but is typically constant during normal operation.

The outputs of weighted buffer 441, and weighted buffers 435-437 areinput to analog summer 411. The output of analog summer 411 is input toPAM-4 sampler 420. The output of analog summer 411 is input to thenon-inverting inputs of samplers 421-423. The inverting input of sampler421 receives reference voltage Vref1. The inverting input of sampler 422receives reference voltage Vref2. The inverting input of sampler 423receives reference voltage Vref3. Reference voltages Vref1, Vref2, andVref3 are typically selected to be between PAM-4 voltage levels. Forexample, if the four PAM-4 levels are −3V, −1V, +1V, and +3V, Vref1 maybe selected to be −2V, Vref2=0V, and Vref3=+2V.

Samplers 421-423 each receive a timing reference CK. CK determines thetiming that samplers 421-423 compare inputs (i.e., output of summer 411)to their respective reference voltage (e.g., Vref1, etc.) to producetheir respective digital output signal. Weighted buffer 441, summer 411,PAM-4 sampler 420, and weighted buffers 435-437 form a combination ISIpre-filter and first DFE tap loop.

The voltage at the input of PAM-4 sampler 420 can be expressed by theEquations in Table 4. In Table 4, v_(m) is the received voltage; m isthe time index; h_(o), h₁, h₂, etc. are the discrete-time voltage valuesof the channel (e.g., interconnect system 140) single-bit response; anda_(m) is the m^(th) transmitted symbol. Note that the equations in Table4 are written for a sample single-tap (i.e. h₀ is main tap and h₁ is thefirst post-cursor) channel.

TABLE 4 define Δ= 0.5(a_(m−1) − a_(m)) v_(m) = a_(m)h₀ + Δh₁ samplerinput: v_(m) − 0.5(a_(m−1)h₀ − v_(m))α₁ sampler input: a_(m)h₀ + Δ(h₁ −h₀α₁) + 0.5Δh₁α₁ (during adaptation) sampler input: a_(m)h₀ + 0.5Δα₁h₁(steady state as α₁ → h₁/h₀

FIG. 4B illustrates a non-speculative DFE PAM-2 receiver with acombination receive FFE and first tap DFE loop. Receiver 402 illustratedin FIG. 4B may correspond to one or more of receiver 150, receivers 214,and/or receivers 224. In an embodiment, receiver 402 may be configuredto implement DFE tap values as described herein. In particular, receiver402 may implement DFE tap values as given in one or more of Equation 1,Equation 2, Table 1, and/or Table 2.

Receiver 402 comprises analog summer 411, weighted buffer 441, weightedbuffer 436, and sampler 422. Thus, it should be evident from FIG. 4Bthat receiver 402 is similar to receiver 400 but without sampler 421,sampler 423, weighted buffer 435, and weighted buffer 437. Also,receiver 402 has the inverting input of sampler 322 coupled to Vref4. Inan embodiment, Vref4=Vref2=0V.

FIG. 5 illustrates a non-speculative DFE receiver with analog FFE andhigher order DFE taps. Receiver 500 illustrated in FIG. 5 may correspondto one or more of receiver 150, receivers 214, and/or receivers 224. Inan embodiment, receiver 500 may be configured to implement DFE tapvalues as described herein. In particular, receiver 500 may implementDFE tap values as given in one or more of Equation 1, Equation 2, Table1, and/or Table 2.

Receiver 500 comprises analog summer 510, receiver feed-forwardequalizer (RxFFE) 545, sampler 520, weighted buffer 532, weighted buffer533, weighted buffer 534, tap logic 552, tap logic 553, tap logic 554,register 562, register 563, and register 564. In an embodiment, sampler520 is a PAM-4 sampler (e.g., similar to, or the same as, PAM-4 sampler320 or 420) and outputs a plurality of decision bits accordingly. Inanother embodiment, sampler 520 is a PAM-2 sampler that outputs a singledecision bit (e.g., similar to, or the same as, sampler 322 or sampler422.) RxFFE 545 includes sample-and-hold (S/H) circuit 540, weightedbuffer 541, weighted buffer 542, and analog summer 511.

An input signal (IN) is operatively coupled to an input of summer 510.Input signal (IN) may be received from, for example, interconnect system140. The output of summer 510 is input to sample-and-hold circuit 540and weighted buffer 542. Weighted buffer 542 outputs the analog voltageat the input to weighted buffer 542 multiplied by the factor K0. In anembodiment, K0=1+0.5α₁, where α₁ is adapted or selected to remove thefirst post-cursor ISI component. When α1 is dynamically adapted, itshould be understood that K0 may be variable during an adaptation (i.e.,training) period, but is typically constant during normal operation.

The output of S/H 540 is input to weighted buffer 541. Weighted buffer541 outputs the analog voltage at the input to weighted buffer 541multiplied by the factor K1. In an embodiment, K1=−0.5α₁. Similar to K0,it should be understood that K1 may be variable during an adaptation(i.e., training) period, but is typically constant during normaloperation.

The outputs of weighted buffer 541 and weighted buffer 542 are input toanalog summer 511. The output of analog summer 511 is input to sampler520. Sampler 520 and each of registers 562-564 receive a timingreference (not shown in FIG. 5.) This timing reference (e.g., CK ofFIGS. 3A and 3B) determines the timing that sampler 520 compares itsinput (i.e., output of summer 511) to reference (or threshold)voltage(s) to produce respective digital output signal(s). The timingreference also determines when each register latches and propagates thevalue on its input to its output. Register 562 receives the output ofsampler 520. Registers 563-564 each serially receive the output of theprevious register 562-564, respectively, thereby forming a serial shiftregister that, for each successive stage, holds previous values sampledby sampler 520.

The output of sampler 520 is also input to tap logic 552. Tap logic 552subtracts the output of sampler 520 from the output of register 562. Theoutput of tap logic 552 is input to weighted buffer 532. Weighted buffer532 outputs the analog voltage at the input to weighted buffer 532multiplied by the factor −K2. In an embodiment, K2=0.5α₂. The output ofweighted buffer 532 is input to summer 510 thereby completing the secondDFE tap loop. The output of register 562 is also input to tap logic 553.Tap logic 553 subtracts the output of register 562 from the output ofregister 563. The output of tap logic 553 is input to weighted buffer533. Weighted buffer 533 outputs the analog voltage at the input toweighted buffer 533 multiplied by the factor −K3. In an embodiment,K3=0.5α₃. The output of weighted buffer 533 is input to summer 510thereby completing the third DFE tap loop. The output of register 563 isalso input to tap logic 554. Tap logic 554 subtracts the output ofregister 563 from the output of register 564. The output of tap logic554 is input to weighted buffer 534. Weighted buffer 534 outputs theanalog voltage at the input to weighted buffer 534 multiplied by thefactor −K4. In an embodiment, K4=0.5α₄. The output of weighted buffer534 is input to summer 510 thereby completing the fourth DFE tap loop.Additional higher order DFE tap loops can be formed in a similar manner.

FIG. 6 illustrates a non-speculative DFE receiver with receive FFE andhigher order DFE taps. Receiver 600 illustrated in FIG. 6 may correspondto one or more of receiver 150, receivers 214, and/or receivers 224. Inan embodiment, receiver 600 may be configured to implement DFE tapvalues as described herein. In particular, receiver 600 may implementDFE tap values as given in one or more of Equation 1, Equation 2, Table1, and/or Table 2.

Receiver 600 comprises analog summer 610, ISI pre-filter/1^(st) DFE tap646, weighted buffer 632, weighted buffer 633, weighted buffer 634, taplogic 652, tap logic 653, tap logic 654, register 662, register 663, andregister 664. ISI pre-filter/1^(st) DFE tap 646 includes weighted buffer641, weighted buffer 642, analog summer 611, and sampler 620. In anembodiment, sampler 620 is a PAM-4 sampler (e.g., similar to, or thesame as, PAM-4 sampler 320 or 420) and outputs a plurality of decisionbits accordingly. In another embodiment, sampler 620 is a PAM-2 samplerthat outputs a single decision bit (e.g., similar to, or the same as,sampler 322 or sampler 422.)

An input signal (IN) is operatively coupled to an input to summer 610.Input signal (IN) may be received from, for example, interconnect system140. The output of summer 610 is input to ISI pre-filter/1^(st) DFE tap646. In particular, the output of summer 610 is input to weighted buffer641. Weighted buffer 641 outputs the analog voltage at the input toweighted buffer 641 multiplied by the factor K0. In an embodiment,K0=1+0.5α₁, where α₁ is adapted or selected to remove the firstpost-cursor ISI component. When α1 is dynamically adapted, it should beunderstood that K0 may be variable during an adaptation (i.e., training)period, but is typically constant during normal operation.

The outputs of weighted buffer 641 and weighted buffer 642 are input toanalog summer 611. The output of analog summer 611 is input to sampler620. The output of sampler 620 is input to weighted buffer 642. Weightedbuffer 642 outputs the analog voltage at the input to weighted buffer642 multiplied by the factor −K1. In an embodiment, K1=0.5α₁. Similar toK0, it should be understood that K1 may be variable during an adaptation(i.e., training) period, but is typically constant during normaloperation.

Sampler 620 and each of registers 662-664 receive a timing reference(not shown in FIG. 6.) This timing reference (e.g., CK of FIGS. 3A and3B) determines the timing that sampler 620 compares its input (i.e.,output of summer 611) to reference (or threshold) voltage(s) to producerespective digital output signal(s). Register 662 receives the output ofsampler 620. Registers 663-664 each serially receive the output of theprevious register 662-664, respectively, thereby forming a serial shiftregister that, for each successive stage, holds previous values sampledby sampler 620.

The output of sampler 620 is also input to tap logic 652. Tap logic 652subtracts the output of sampler 620 from the output of register 662. Theoutput of tap logic 652 is input to weighted buffer 632. Weighted buffer632 outputs the analog voltage at the input to weighted buffer 632multiplied by the factor −K2. In an embodiment, K2=0.5α₂. The output ofweighted buffer 633 is input to summer 610 thereby completing the secondDFE tap loop. The output of register 662 is also input to tap logic 653.Tap logic 653 subtracts the output of register 662 from the output ofregister 663. The output of tap logic 653 is input to weighted buffer633. Weighted buffer 633 outputs the analog voltage at the input toweighted buffer 633 multiplied by the factor −K3. In an embodiment,K3=0.5α₃. The output of weighted buffer 633 is input to summer 610thereby completing the third DFE tap loop. The output of register 663 isalso input to tap logic 654. Tap logic 654 subtracts the output ofregister 663 from the output of register 664. The output of tap logic654 is input to weighted buffer 634. Weighted buffer 634 outputs theanalog voltage at the input to weighted buffer 634 multiplied by thefactor −K4. In an embodiment, K4=0.5α₄. The output of weighted buffer634 is input to summer 610 thereby completing the fourth DFE tap loop.Additional higher order DFE tap loops can be formed in a similar manner.

FIG. 7 illustrates a non-speculative DFE receiver with low-latency DFEtap feedback. Receiver 700 illustrated in FIG. 7 may correspond to oneor more of receiver 150, receivers 214, and/or receivers 224. In anembodiment, receiver 700 may be configured to implement DFE tap valuesas described herein. In particular, receiver 700 may implement DFE tapvalues as given in one or more of Equation 1, Equation 2, Table 1,and/or Table 2.

Receiver 700 comprises analog summer 710, ISI pre-filter/1^(st) DFE tap746, weighted buffer 732, weighted buffer 733, weighted buffer 734,weighted buffer 735, register 762, and register 763. ISIpre-filter/1^(st) DFE tap 746 includes weighted buffer 741, weightedbuffer 742, analog summer 711, and sampler 720. In an embodiment,sampler 720 is a PAM-4 sampler (e.g., similar to, or the same as, PAM-4sampler 320 or 420) and outputs a plurality of decision bitsaccordingly. In another embodiment, sampler 720 is a PAM-2 sampler thatoutputs a single decision bit (e.g., similar to, or the same as, sampler322 or sampler 422.)

An input signal (IN) is operatively coupled to an input of summer 710.Input signal (IN) may be received from, for example, interconnect system140. The output of summer 710 is input to ISI pre-filter/1^(st) DFE tap746. In particular, the output of summer 710 is input to weighted buffer741. Weighted buffer 741 outputs the analog voltage at the input toweighted buffer 741 multiplied by the factor K0. In an embodiment,K0=1+0.5α₁, where α₁ is adapted or selected to remove the firstpost-cursor ISI component. When α₁ is dynamically adapted, it should beunderstood that K0 may be variable during an adaptation (i.e., training)period, but is typically constant during normal operation.

The outputs of weighted buffer 741 and weighted buffer 742 are input toanalog summer 711. The output of analog summer 711 is input to sampler720. The output of sampler 720 is input to weighted buffer 742. In anembodiment, K1=0.5α₁. Similar to K0, it should be understood that K1 maybe variable during an adaptation (i.e., training) period, but istypically constant during normal operation.

Sampler 720 and each of registers 762-764 receive a timing reference(not shown in FIG. 7.) This timing reference (e.g., CK of FIGS. 3A and3B) determines the timing that sampler 720 compares its input (i.e.,output of summer 711) to reference (or threshold) voltage(s) to producerespective digital output signal(s). Register 762 receives the output ofsampler 720. Registers 763 etc. each serially receive the output of theprevious register 762-763, respectively thereby forming a serial shiftregister that, for each successive stage, holds previous values sampledby sampler 720.

The output of sampler 720 is also input to weighted buffer 732. Weightedbuffer 732 outputs the analog voltage at the input to weighted buffer732 multiplied by the factor +K2. The output of register 762 is input toweighted buffer 733. Weighted buffer 733 outputs the analog voltage atthe input to weighted buffer 733 multiplied by the factor −K2. In anembodiment, K2=0.5α₂. The output of weighted buffer 732 and the outputof weighted buffer 732 are input to summer 710 thereby completing thesecond DFE tap loop. The output of register 762 is also input toweighted buffer 734. Weighted buffer 734 outputs the analog voltage atthe input to weighted buffer 734 multiplied by the factor +K3. Theoutput of weighted buffer 734 and the output of weighted buffer 735(which receives the output of register 763—not shown in FIG. 7) areinput to summer 710 thereby completing the third DFE tap loop.Additional higher order DFE tap loops can be formed in a similar manner.

FIG. 8 illustrates a PAM-4 receiver with low-latency DFE feedback.Receiver 800, illustrated in FIG. 8, may correspond to one or more ofreceiver 150, receivers 214, and/or receivers 224. In an embodiment,receiver 800 may be configured to implement DFE tap values as describedherein. In particular, receiver 800 may implement DFE tap values asgiven in one or more of Equation 1, Equation 2, Table 1, and/or Table 2.

Receiver 800 comprises analog summer 810, sampler 821, sampler 822,sampler 823, weighted buffer 831, weighted buffer 832, and weightedbuffer 833. Weighted buffers 831-833 receive digital signals that areinterpreted to be +1 or −1. Weighted buffers 831-833 apply (e.g.,multiply) a weighting factor (−α) to the input value and output ananalog voltage corresponding to the weighted input signal. For example,when weighted buffer 831 receives a logical “0” (which is interpreted tomean −1), weighted buffer 831 applies the weighting factor of −α andoutput an analog signal corresponding to −1×−α=α volts. When weightedbuffer 831 receives a logical “1” (which is interpreted to mean+1),weighted buffer 831 applies the weighting factor of −α and output ananalog signal corresponding to +1×−α=−α volts.

An input signal (IN) is operatively coupled to an input to summer 810.Input signal (IN) may be received from, for example, interconnect system140. The output of summer 810 is input to PAM-4 sampler 820. The outputof analog summer 810 is input to the non-inverting inputs of samplers821-823. The inverting input of sampler 821 receives reference voltageVref1. The inverting input of sampler 822 receives reference voltageVref2. The inverting input of sampler 823 receives reference voltageVref3. Reference voltages Vref1, Vref2, and Vref3 are typically selectedto be between PAM-4 voltage levels. For example, if the four PAM-4levels are −3V, −1V, +1V, and +3V, Vref1 may be selected to be −2V,Vref2=0V, and Vref3=+2V.

Samplers 821-823 each receive a timing reference CK. CK determines thetiming that samplers 821-823 compare inputs (i.e., output of summer 811)to their respective reference voltage (e.g., Vref1, etc.) to producetheir respective digital output signal. The output of sampler 821 isinput to weighted buffer 831. The output of sampler 822 is input toweighted buffer 832. The output of sampler 823 is input to weightedbuffer 833. Weighted buffers 831-833 each apply (e.g., multiply) thesame weighting factor (i.e., −α) to their respective input value andoutput a respective analog voltage corresponding to the weighted inputsignal. Note that when Vref3>Vref2>Vref1, the outputs OUT[1:3] of PAM-4sampler 820 are encoded as a 3-bit thermometer code. This 3-bitthermometer code is not decoded before being applied to the inputs ofweighted buffers 831-833. This lack of decoding logic helps lower thelatency from the CK timing reference that causes samplers 821-823 tosample to the application of the DFE tap value to summer 810.

FIG. 9 illustrates a PAM-4 receiver with DFE feedback. Receiver 900illustrated in FIG. 9 may correspond to one or more of receiver 150,receivers 214, and/or receivers 224. In an embodiment, receiver 900 maybe configured to implement DFE tap values as described herein. Inparticular, receiver 900 may implement DFE tap values as given in one ormore of Equation 1, Equation 2, Table 1, and/or Table 2.

Receiver 900 comprises analog summer 910, sampler 921, sampler 922,sampler 923, sampler 924, sampler 925, sampler 926, weighted buffer 931,weighted buffer 932, weighted buffer 933, weighted buffer 935, weightedbuffer 936, weighted buffer 937, and sample-and-hold (S/H) 990.

An input signal (IN) is operatively coupled to the input to S/H 990 andthe non-inverting inputs of samplers 925-927. Input signal (IN) may bereceived from, for example, interconnect system 140. The output of S/H990 is input to summer 910. The output of analog summer 910 is input tothe non-inverting inputs of samplers 921-923. The inverting input ofsampler 921 receives reference voltage Vref1. The inverting input ofsampler 922 receives reference voltage Vref2. The inverting input ofsampler 923 receives reference voltage Vref3. The inverting input ofsampler 925 receives reference voltage Vref5. The inverting input ofsampler 926 receives reference voltage Vref6. The inverting input ofsampler 923 receives reference voltage Vref7. Reference voltages Vref1,Vref2, Vref3, Vref5, Vref6, and Vref7 are typically selected to bebetween PAM-4 voltage levels. For example, if the four PAM-4 levels are−3V, −1V, +1V, and +3V, Vref1 and Vref5 may be selected to be −2V,Vref2=Vref6=0V, and Vref3=Vref7=+2V.

Samplers 921-923 and 925-927 each receive a timing reference CK. CKdetermines the timing that samplers 921-923 and 925-927 compare inputs(i.e., the input voltage and the output of summer 910) to theirrespective reference voltage (e.g., Vref1, etc.) to produce theirrespective digital output signal. The output of sampler 921 is input toweighted buffer 931. The output of sampler 922 is input to weightedbuffer 932. The output of sampler 923 is input to weighted buffer 933.The output of sampler 925 is input to weighted buffer 935. The output ofsampler 926 is input to weighted buffer 936. The output of sampler 927is input to weighted buffer 937. Weighted buffers 931-933 each apply(e.g., multiply) the same weighting factor (i.e., −K1) to theirrespective input value and output a respective analog voltagecorresponding to the weighted input signal. In FIG. 9, weighted buffers935-937 each apply (e.g., multiply) the same weighting factor (i.e.,+K_(C)) to their respective input value and output a respective analogvoltage corresponding to the weighted input signal. However, it shouldbe understood that in some embodiments weighted buffers 935-937 apply(e.g., multiply) different weighting factors from each other. Inaddition, in an embodiment, K_(C)=K1. In another embodiment, K_(C)≠K1.

The voltage at the inputs of samplers 931-933 can be expressed by theEquations in Table 5. In Table 5, v_(m) is the received voltage; m isthe time index; h_(o), h₁, h₂, etc. are the discrete-time voltage valuesof the channel (e.g., interconnect system 140) single-bit response; anda_(m) is the m^(th) transmitted symbol.

TABLE 5 define Δ= 0.5(a_(m−1) − a_(m)) v_(m) = a_(m)h₀ + Δh₁ samplerinput: v_(m) − 0.5(a_(m−1)h₀ − a_(m)h₀)α₁ sampler input: a_(m)h₀ + Δ(h₁− h₀α₁) (during adaptation) sampler input: a_(m)h₀ (steady state as α₁ →h₁/h₀)

FIG. 10 illustrates a receiver with DFE feedback. Receiver 1000illustrated in FIG. 10 may correspond to one or more of receiver 150,receivers 214, and/or receivers 224. Receiver 1000 comprises analogsummer 1010, sampler 1021, sampler 1022, weighted buffer 1031, weightedbuffer 1032, and sample-and-hold (S/H) 1090. In an embodiment, samplers1021-1022 may be PAM-2 samplers. In another embodiment, samplers1021-1022 may be PAM-4 samplers.

An input signal (IN) is operatively coupled to the input to S/H 1090 andthe input of sampler 1021. Input signal (IN) may be received from, forexample, interconnect system 140. The output of S/H 1090 is input tosummer 1010. The output of analog summer 1010 is input to sampler 1022.

Samplers 1021-1023 and 1025-1027 each receive a timing reference (notshown in FIG. 10.) The output of sampler 1021 is input to weightedbuffer 1031. The output of sampler 1022 is input to weighted buffer1032. The output of sampler 1022 is the output of receiver 1000 OUT.Weighted buffer 1031 applies (e.g., multiplies) a first weighting factor(i.e., +K) to its respective input value and outputs a respective analogvoltage corresponding to the weighted input signal. Weighted buffer 1022applies (e.g., multiplies) a second weighting factor (i.e., −K) to itsrespective input value and outputs a respective analog voltagecorresponding to the weighted input signal.

FIG. 11 illustrates a receiver with higher order DFE feedback. Receiver1100 illustrated in FIG. 11 may correspond to one or more of receiver150, receivers 214, and/or receivers 224. Receiver 1100 comprises analogsummer 1110, 1^(st) DFE tap 1146, weighted buffer 1132, weighted buffer1133, weighted buffer 1134, tap logic 1152, tap logic 1153, tap logic1154, register 1162, register 1163, and register 1164. 1^(st) DFE tap1146 includes analog summer 1111, sampler 1121, sampler 1122, weightedbuffer 1131, weighted buffer 1132, and sample-and-hold (S/H) 1190. In anembodiment, sampler 1120 is a PAM-4 sampler (e.g., similar to, or thesame as, PAM-4 sampler 320 or 420) and outputs a plurality of decisionbits accordingly. In another embodiment, sampler 1120 is a PAM-2 samplerthat outputs a single decision bit (e.g., similar to, or the same as,sampler 322 or sampler 422.)

An input signal (IN) is operatively coupled to an input to summer 1110.Input signal (IN) may be received from, for example, interconnect system140. The output of summer 1110 is input to 1^(st) DFE tap 1146. Inparticular, the output of summer 1110 is input to S/H 1190 and sampler1121.

The outputs of weighted buffer 1131 and weighted buffer 1132 are inputto analog summer 1111. The output of analog summer 1111 is input tosampler 1122. The output of sampler 1122 is input to tap logic 1152.

Sampler 1122, sampler 1121, and each of registers 1162-1164 receive atiming reference (not shown in FIG. 11.) This timing reference (e.g., CKof FIGS. 3A and 3B) determines the timing that sampler 1122 compares itsinput (i.e., output of summer 1111) to reference (or threshold)voltage(s) to produce respective digital output signal(s). Registers1163-1164 each serially receive the output of the previous register1162-1163, respectively, thereby forming a serial shift register that,for each successive stage, holds previous values sampled by sampler1122.

The output of sampler 1122 is also input to tap logic 1152. Tap logic1152 subtracts the output of register 1162 from the output of sampler1122. The output of tap logic 1152 is input to weighted buffer 1132.Weighted buffer 1132 outputs the analog voltage at the input to weightedbuffer 1132 multiplied by the factor −K2. In an embodiment, K2=0.5α₂.The output of weighted buffer 1132 is input to summer 1110 therebycompleting the second DFE tap loop. The output of register 1162 is alsoinput to tap logic 1153. Tap logic 1153 subtracts the output of register1163 from the output of register 1162. The output of tap logic 1153 isinput to weighted buffer 1133. Weighted buffer 1133 outputs the analogvoltage at the input to weighted buffer 1133 multiplied by the factor−K3. In an embodiment, K3=0.5α₃. The output of weighted buffer 1133 isinput to summer 1110 thereby completing the third DFE tap loop. Theoutput of register 1163 is also input to tap logic 1154. Tap logic 1154subtracts the output of register 1164 from the output of register 1163.The output of tap logic 1154 is input to weighted buffer 1134. Weightedbuffer 1134 outputs the analog voltage at the input to weighted buffer1132 multiplied by the factor −K4. In an embodiment, K4=0.5α₄. Theoutput of weighted buffer 1134 is input to summer 1110 therebycompleting the fourth DFE tap loop. Additional higher order DFE taploops can be formed in a similar manner.

FIG. 12 illustrates a communication system with non-uniform transmitequalization and speculative DFE. Communication system 1200 comprises adriving integrated circuit, a receiving integrated circuit, andinterconnect between them. The driving integrated circuit includestransmitter circuit 1210 (a.k.a., a driver). Transmit finite impulseresponse (FIR) logic 1275 controls transmitter circuit 1210 to implementnon-uniform transmit equalization.

The receiver integrated circuit includes receiver circuit 1250. Theinterconnect between the driving integrated circuit and the receivingintegrated circuit comprises interconnect system 1240. Interconnectsystem 1240 would typically comprise a printed circuit (PC) board,connector, cable, flex circuit, other substrate, and/or a combination ofthese. Interconnect system 1240 may be and/or include one or moretransmission lines.

Receiver circuit 1250 would typically be part of an integrated circuitthat is receiving the signal sent by the driving integrated circuit. Itshould be understood that termination (not shown in FIG. 12) can be partof the integrated circuit or interconnect system 1240. It should also beunderstood that although system 1200 is illustrated as transmitting asingle-ended signal, the signals sent by the driving integrated circuitof system 1200 may represent one of a pair of differential signals orone of a collection of signals sending multi-wire-coded data.

In FIG. 12, the output of transmitter circuit 1210 is connected to afirst end of interconnect system 1240. The second end of interconnectsystem 1240 is connected to the input of receiver 1250. Transmittercircuit 1210 is configured to drive PAM-4 signaling levels.

In an embodiment, receiver 1250 is a speculative DFE receiver. FIR logic1275 applies non-uniform pre-emphasis to a PAM-4 output signal. Thenon-uniform pre-emphasis output by transmitter circuit 1210 under thecontrol of FIR logic 1275 is selected such that, after passing throughinterconnect system 1420, a number of the received PAM-4 voltage levelshave effectively the same values even when the previous symbols aredifferent. For example, with uniform pre-emphasis (or no pre-emphasis)the non-ideal characteristics (e.g., ISI) of interconnect system 1240may result in as many as 13 voltage levels (but still only representing4 PAM-4 symbols) arriving at receiver 1250. The non-uniform emphasisapplies by FIR logic 1275 reduces the number of different voltage levelsarriving at the input to receiver 1250. Thus, in an embodiment, thenon-uniform pre-emphasis allows certain PAM-4 transitions sent bytransmitter circuit 1210 to be accurately sampled by speculative DFEreceiver 1250 using a reduced number of comparators. For example, byapplying appropriate non-uniform pre-emphasis, the number of voltagelevels arriving at receiver 1250 can be reduced from 13 voltage levels(which requires 12 comparators to sample) to 6 voltage levels (which canbe sampled with 5 comparators).

FIG. 13A illustrates an example of non-uniform transmit equalization. InFIG. 13A, a piecewise-linear approximation of the signal output bytransmitter 1210 (under the control of FIR logic 1275) for two examplePAM-4 transitions is shown—from −1 to +3 and from −3 to +3. Theequalized PAM-4 transition from −3 to +3 is shown as a transition fromthe −3 voltage level to a +3+α voltage level. The equalized PAM-4transition from −1 to +3 is shown as a simple transition from the −1voltage level to the +3 voltage level. Thus, since the symbol after bothof these transition is a +3 PAM-4 symbol, it can be seen that FIR logic1275 is applying non-uniform pre-emphasis.

After passing through the channel (i.e., interconnect system 1240),bandwidth limitations, non-linearity's and other non-ideal properties ofinterconnect system 1240 result in the illustrated sketches shown on theright of FIG. 13A. Although both of these sketches illustrate the samewaveform, one of the waveforms is sketched as a piecewise linearapproximation. This is done to better illustrate the results of thenon-linear equalization at the receiver. In particular, even though bothtransitions started from different states (i.e., −1 and −3) in theprevious symbol period, both transitions (i.e., −1+3 and −3 to +3)result in substantially the same voltage at the sampling time for thenext symbol period. In FIG. 13A, that voltage is +3−2α.

Also shown in FIG. 13A, is a suitable reference (or threshold) voltage(V_(+2b)) to be used to determine whether the resulting symbolcorresponds to a PAM-4+3 level. V_(+2b) is illustrated to be +2−2α.

FIG. 13B illustrates another example of non-uniform transmitequalization. In FIG. 13B, a piecewise-linear approximation of thesignal output by transmitter 1210 (under the control of FIR logic 1275)for two additional example PAM-4 transitions is shown—from −1 to +1 andfrom −3 to +1. The equalized PAM-4 transition from −3 to +1 is shown asa transition from the −3 voltage level to a +1+2α voltage level. Theequalized PAM-4 transition from −1 to +1 is shown as a transition fromthe −1 voltage level to a +1+α voltage level. Thus, since the symbolafter both of these transition is a +3 PAM-4 symbol, it can be seen thatFIR logic 1275 is applying non-uniform pre-emphasis.

After passing through the channel (i.e., interconnect system 1240),bandwidth limitations, non-linearity's and other non-ideal properties ofinterconnect system 1240 result in the illustrated sketches shown on theright of FIG. 13B. Even though both transitions started from differentstates (i.e., −1 and −3) in the previous symbol period, both transitions(i.e., −1 to +3 and −3 to +3) result in substantially the same voltageat the sampling time for the next symbol period. In FIG. 13B, thatvoltage is +1. Also shown in FIG. 13B, is a suitable reference (orthreshold) voltage (V₀) to be used to determine whether the resultingsymbol corresponds to a positive (+1 or +3) or a negative (−1 or −3)PAM-4 level. V₀ is illustrated to be 0 V.

FIG. 13C is a diagram illustrating the transmit levels (voltages) thatresult from all of the possible PAM-4 transitions, corresponding receivelevels, and suitable threshold levels to distinguish the receive levels.The transitions and levels illustrated in FIG. 13C are also given inTable 6. As can be seen from FIG. 13C and Table 6, the suitable numberof threshold levels is five. Thus, for these signals that havenon-uniform pre-emphasis, only five comparators/samplers would be neededto implement a speculative PAM-4 DFE receiver.

TABLE 6 Previous Current Tx FIR tap Tx signal Rx signal Suitable SymbolSymbol value level level threshold +3 +3 0 +3 +3 +2 +3 +1  −α +1 − α +1+2 +3 −1 −2α  −1 − 2α −1  0 +3 −3  −α −3 − α −3 + 2α −2 + 2α +1 +3  +α+3 + α +3 +2 +1 +1 0 +1 +1  0 +1 −1  −α −1 − α −1  0 +1 −3 0 −3 −3 + 2α−2 + 2α −1 +3 0 +3 +3 − 2α +2 − 2α −1 +1  +α +1 + α +1  0 −1 −1 0 −1 −1 0 −1 −3  −α −3 − α −3 −2 −3 +3  +α +3 + α +3 − 2α +2 − 2α −3 +1 +2α +1 + 2α +1  0 −3 −1 α −1 + α −1 −2 −3 −3 0 −3 −3 −2

It should be noted that for positive previous symbols (i.e., +1 or +3),there are only three suitable threshold voltages given: V_(−2b)=−2+2α;V₀=0, and V₊₂=+2. FIG. 14A illustrates PAM-4 data eyes for non-uniformlyequalized transitions from positively signed previous symbols. Fornegative previous symbols (i.e., −1 or −3), there are also only threesuitable threshold voltages given: V⁻²=−2, V₀=0, and V_(−2b)=+2−2α. FIG.14B illustrates PAM-4 data eyes for non-uniformly equalized transitionsfrom negatively signed previous symbols. Note also that the thresholdvoltage V₀=0 is used for both positive and negative previous symbols.Thus, the sampler with a threshold voltage of V₀=0 can be used todetermine which set of samplers or threshold voltages (i.e., the setwith V_(−2b), V₀, and V₊₂, or the set with V⁻², V₀, and V_(+2b)) shouldbe used to determine the current symbol.

FIG. 15 illustrates a PAM-4 speculative DFE receiver with fivecomparators. Receiver 1500, illustrated in FIG. 15, may correspond toone or more of receiver 150, receivers 214, and/or receivers 224.Receiver 1500 comprises samplers 1523-1527, register 1560, multiplexer(MUX) 1580, MUX 1581, and decoding logic 1585. In FIG. 15, an inputsignal (IN) is operatively coupled to the non-inverting inputs ofsamplers 1523-1527. The inverting input (i.e., reference or thresholdvoltage input) of sampler 1523 receives reference voltage V⁻². Theinverting input of sampler 1524 receives reference voltage V_(−2b). Theinverting input of sampler 1525 receives reference voltage V₀. Theinverting input of sampler 1526 receives reference voltage V_(+2b). Theinverting input of sampler 1527 receives reference voltage V₊₂.

Samplers 1523-1527 each receive a timing reference CK. CK determines thetiming that samplers 1523-1527 compare inputs (i.e., IN) to theirrespective reference voltage (e.g., V⁻², V_(−2b), etc.) to produce theirrespective digital output signal. The timing reference also determineswhen register 1560 latches and propagates the value on its input to itsoutput. The output of sampler 1523 (OUT−2) is input to the “0” input ofMUX 1580. The output of sampler 1524 (OUT−2B) is input to the “1” inputof MUX 1580. The output of sampler 1525 (OUT0) is input to logic 1585and the input of register 1560. The output of sampler 1526 (OUT+2B) isinput to the “0” input of MUX 1581. The output of sampler 1527 (OUT+2)is input to the “1” input of MUX 1581.

The select inputs (“S”) of MUX 1580 and MUX 1581 are received from theoutput of register 1560. Thus, the output of register 1560 is the resultof the comparison by sampler 1525 of the input signal to the referencevoltage V₀. Since V₀ is between the PAM-4 levels of +1 and −1, theoutput of register 1560 corresponds to the sign of the previous symbol.In other words, when the previous symbol is a −1 or a −3, the output ofregister 1560 controls MUXs 1580-1581 to select their “0” input. Whenthe previous symbol is a +1 or a +3, the output of register 1560controls MUXs 1580-1581 to select their “1” input. The outputs of MUXs1580-1581 are received by logic 1585 to produce a received valueOUT[0:1].

When the previous symbol is a −1 or a −3 (based on the output ofregister 1560), logic 1585 decodes the results of comparisons between INand reference voltages V⁻², V₀, and V_(+2b). When the previous symbol isa −1 or a −3 (based on the output of register 1560), logic 1585 decodesthe results of comparisons between IN and reference voltages V_(−2b),V₀, and V₊₂. In an embodiment, V_(−2b), V⁻², V₀, V_(+2b), and V₊₂ areselected in accordance with the relative (to each other) voltage levelsof V⁻²=−2, V_(−2b)=−2+2α; V₀=0, V_(−2b)=+2−2α, and V₊₂=+2.

FIG. 16 illustrates a PAM-4 speculative DFE receiver with second tapfeedback. Receiver 1600, illustrated in FIG. 16, may correspond to oneor more of receiver 150, receivers 214, and/or receivers 224. Receiver1600 comprises analog summer 1611, samplers 1623-1627, tap logic 1652,weighted buffer 1651, register 1660, register 1661, multiplexer (MUX)1680, MUX 1681, and decoding logic 1685. In FIG. 16, an input signal(IN) is input to analog summer 1611. The output of analog summer 1611 isinput to the non-inverting inputs of samplers 1623-1627. The invertinginput (i.e., reference or threshold voltage input) of sampler 1623receives reference voltage V⁻². The inverting input of sampler 1624receives reference voltage V_(−2b). The inverting input of sampler 1625receives reference voltage V₀. The inverting input of sampler 1626receives reference voltage V_(+2b). The inverting input of sampler 1627receives reference voltage V₊₂.

Samplers 1623-1627 each receive a timing reference CK. CK determines thetiming that samplers 1623-1627 compare inputs (i.e., IN) to theirrespective reference voltage (e.g., V⁻², V_(−2b), etc.) to produce theirrespective digital output signal. The timing reference also determineswhen registers 1660 and 1661 latch and propagate the value on theirrespective inputs to their respective outputs. The output of sampler1623 (OUT−2) is input to the “0” input of MUX 1680. The output ofsampler 1624 (OUT−2B) is input to the “1” input of MUX 1680. The outputof sampler 1625 (OUT0) is input to logic 1685 and the input of register1660. The output of sampler 1626 (OUT+2B) is input to the “0” input ofMUX 1681. The output of sampler 1627 (OUT+2) is input to the “1” inputof MUX 1681.

The select inputs (“S”) of MUX 1680 and MUX 1681 are received from theoutput of register 1660. Thus, the output of register 1660 is the resultof the comparison by sampler 1625 of the input signal to the referencevoltage V₀. Since V₀ is between the PAM-4 levels of +1 and −1, theoutput of register 1660 corresponds to the sign of the previous symbol.In other words, when the previous symbol is a −1 or a −3, the output ofregister 1660 controls MUXs 1680-1581 to select their “0” input. Whenthe previous symbol is a +1 or a +3, the output of register 1660controls MUXs 1680-1681 to select their “1” input. The outputs of MUXs1680-1681 are received by logic 1685 to produce a received valueOUT[0:1].

The output of logic 1685 OUT[0:1] is input to register 1661 and taplogic 1652. The output of register 1661 is input to tap logic 1652. Taplogic 1652 subtracts the output of register 1661 from the output oflogic 1685. The output of tap logic 1652 is input to weighted buffer1651. The output of weighted buffer 1651 is input to summer 1611 therebycompleting a 2^(nd) tap DFE loop. In an embodiment, V_(−2b), V⁻², V₀,V_(+2b), and V₊₂ are selected in accordance with the relative (to eachother) voltage levels of V⁻²=−2, V_(−2b)=−2+2α; V₀=0, V_(−2b)=+2−2α, andV₊₂=+2.

FIG. 17 illustrates a PAM-4 speculative DFE receiver having second tapfeedback without subtraction. Receiver 1700, illustrated in FIG. 17, maycorrespond to one or more of receiver 150, receivers 214, and/orreceivers 224. Receiver 1700 comprises samplers analog summer 1711,1723-1727, register 1763, register 1765, register 1767, register 1768,multiplexer (MUX) 1780, MUX 1781, decoder logic 1785, tap logic 1788,and digital-to-analog converter(s) 1798. In FIG. 17, an input signal(IN) is input to analog summer 1711. The output of analog summer 1711 isinput to the non-inverting inputs of samplers 1723-1727. The invertinginput (i.e., reference or threshold voltage input) of sampler 1723receives reference voltage V⁻². The inverting input of sampler 1724receives reference voltage V_(−2b). The inverting input of sampler 1725receives reference voltage V₀. The inverting input of sampler 1726receives reference voltage V_(+2b). The inverting input of sampler 1727receives reference voltage V₊₂.

Samplers 1723-1727 each receive a timing reference CK. CK determines thetiming that samplers 1723-1727 compare inputs (i.e., IN) to theirrespective reference voltage (e.g., V⁻², V_(−2b), etc.) to produce theirrespective digital output signal. The timing reference also determineswhen register 1760 latches and propagates the value on its input to itsoutput. The output of sampler 1723 (OUT−2) is input to the “0” input ofMUX 1780. The output of sampler 1724 (OUT−2B) is input to the “1” inputof MUX 1780. The output of sampler 1725 (OUT0) is input to logic 1785and the input of register 1765. The output of sampler 1726 (OUT+2B) isinput to the “0” input of MUX 1781. The output of sampler 1727 (OUT+2)is input to the “1” input of MUX 1781.

The select inputs (“S”) of MUX 1780 and MUX 1781 are received from theoutput of register 1765. Thus, the output of register 1765 is the resultof the comparison by sampler 1725 of the input signal to the referencevoltage V₀. Since V₀ is between the PAM-4 levels of +1 and −1, theoutput of register 1760 corresponds to the sign of the previous symbol.In other words, when the previous symbol is a −1 or a −3, the output ofregister 1760 controls MUXs 1780-1781 to select their “0” input. Whenthe previous symbol is a +1 or a +3, the output of register 1760controls MUXs 1780-1781 to select their “1” input.

When the previous symbol is a −1 or a −3 (based on the output ofregister 1760), logic 1785 decodes the results of comparisons between INand reference voltages V⁻², V₀, and V_(+2b). When the previous symbol isa −1 or a −3 (based on the output of register 1765), logic 1785 decodesthe results (delayed by one symbol period by registers 1763, 1765, and1767) of comparisons between IN and reference voltages V_(−2b), V₀, andV₊₂. In an embodiment, V_(−2b), V⁻², V₀, V_(+2b), and V₊₂ are selectedin accordance with the relative (to each other) voltage levels ofV⁻²=−2, V_(31 2b)=−2+2α; V₀=0, V_(−2b)=+2−2α, and V₊₂=+2.

The output of MUX 1780 is input to register 1763. The output of MUX 1781is input to register 1767. The output of sampler 1725 is input toregister 1765. Thus, the outputs of register 1763, register 1765, andregister 1767 correspond (in thermometer code) to the previous PAM-4symbol received via IN. The outputs of register 1763, register 1765, andregister 1767 received by logic 1785 to produce a received valueOUT[0:1]. The outputs of register 1763, register 1765, and register 1767are also received by tap logic 1788 to produce a tap value from thecurrent sampled result and the previous symbol. The tap value from logic1788 is input to register 1768. The output of register 1768 is input toDAC(s) 1798. The analog output of DAC(s) 1798 is input to analog summer1711 thereby completing at least a 2^(nd) tap DFE loop.

FIG. 18 is a flowchart illustrating a non-speculative decoder freemethod of decision feedback equalization. The steps illustrated in FIG.18 may be performed by one or more elements of communication system 100,memory system 200, and/or communication system 1200. A first samplerdecision indicator based on a comparison between an equalized datasignal and a first reference voltage is produced (1802). For example,sampler 821 may compare the output of summer 810 to threshold orreference voltage Vref1 to produce a value on OUT[1].

A second sampler decision indicator based on a comparison between anequalized data signal and a second reference voltage is produced (1804).For example, sampler 822 may compare the output of summer 810 tothreshold or reference voltage Vref2 to produce a value on OUT[2]. Athird sampler decision indicator based on a comparison between anequalized data signal and a third reference voltage is produced (1806).For example, sampler 823 may compare the output of summer 810 tothreshold or reference voltage Vref3 to produce a value on OUT[3].

Based on the first sampler decision indicator, a first error removalvoltage is produced (1808). For example, based on OUT[1], weightedbuffer 831 may produce an analog error removal voltage that is suppliedto summer 810. Based on the second sampler decision indicator, a seconderror removal voltage is produced (1810). For example, based on OUT[2],weighted buffer 831 may produce an analog error removal voltage that issupplied to summer 810. Based on the third sampler decision indicator, athird error removal voltage is produced (1812). For example, based onOUT[3], weighted buffer 831 may produce an analog error removal voltagethat is supplied to summer 810.

The received data signal is summed with the first error removal voltage,the second error removal voltage, and the third error removal voltage toproduce the equalized data signal (1814). For example, the output ofweighted buffer 831, the output of weighted buffer 832, and the outputof weighted buffer 833 are summed with the input IN to produce anequalized data signal that is supplied to samplers 821-823.

FIGS. 19A-19B are a flowchart illustrating a non-speculative method ofdecision feedback equalization. The steps illustrated in FIGS. 19A-19Bmay be performed by one or more elements of communication system 100and/or memory system 200. A first previous symbol sampler decisionindicator based on a comparison between an equalized data signal and afirst reference voltage is produced (1902). For example, sampler 921 maycompare the output of summer 910 to threshold or reference voltage Vref1to produce a value on OUT[1]. A second previous symbol sampler decisionindicator based on a comparison between an equalized data signal and asecond reference voltage is produced (1904). For example, sampler 922may compare the output of summer 910 to threshold or reference voltageVref2 to produce a value on OUT[2]. A third previous symbol samplerdecision indicator based on a comparison between an equalized datasignal and a third reference voltage is produced (1906). For example,sampler 923 may compare the output of summer 910 to threshold orreference voltage Vref3 to produce a value on OUT[3].

A first current symbol sampler decision indicator based on a comparisonbetween a received data signal and the first reference voltage isproduced (1908). For example, sampler 925 may compare input voltage INto threshold or reference voltage Vref1 to produce a value on that isinput to weighted buffer 935. A second current symbol sampler decisionindicator based on a comparison between a received data signal and thesecond reference voltage is produced (1910). For example, sampler 926may compare input voltage IN to threshold or reference voltage Vref2 toproduce a value on that is input to weighted buffer 936. A third currentsymbol sampler decision indicator based on a comparison between areceived data signal and the third reference voltage is produced (1912).For example, sampler 927 may compare input voltage IN to threshold orreference voltage Vref3 to produce a value on that is input to weightedbuffer 937.

Based on the first previous symbol sampler decision indicator, a firstprevious symbol error removal voltage is produced (1914). For example,based on the input from sampler 921, weighted buffer 931 may produce anerror removal voltage to be supplied to summer 910. Based on the secondprevious symbol sampler decision indicator, a second previous symbolerror removal voltage is produced (1916). For example, based on theinput from sampler 922, weighted buffer 932 may produce an error removalvoltage to be supplied to summer 910. Based on the third previous symbolsampler decision indicator, a third previous symbol error removalvoltage is produced (1918). For example, based on the input from sampler923, weighted buffer 933 may produce an error removal voltage to besupplied to summer 910.

Based on the first current symbol sampler decision indicator, a firstcurrent symbol error removal voltage is produced (1920). For example,based on the input from sampler 921, weighted buffer 931 may produce anerror removal voltage to be supplied to summer 910. Based on the secondcurrent symbol sampler decision indicator, a second current symbol errorremoval voltage is produced (1922). For example, based on the input fromsampler 922, weighted buffer 932 may produce an error removal voltage tobe supplied to summer 910. Based on the third current symbol samplerdecision indicator, a third current symbol error removal voltage isproduced (1924). For example, based on the input from sampler 923,weighted buffer 933 may produce an error removal voltage to be suppliedto summer 910.

A delayed version of a received data signal is summed with the firstprevious symbol error removal voltage, the second previous symbol errorremoval voltage, the third previous symbol error removal voltage, thefirst current symbol error removal voltage, the second current symbolerror removal voltage, and the third current symbol error removalvoltage to produce the equalized data signal (1926). For example, summer910 sums inputs from S/H 990, weighted buffers 931-933, and weightedbuffers 935-937 to produce an equalized data signal that is supplied tosamplers 921-933.

It should be understood that the received data signal IN is notsufficiently equalized when it is input to samplers 925-937. In anembodiment, the signal “IN” may already be equalized using acontinuous-time equalizer (CTLE) and variable-gain-amplifier (VGA), bothof which reside in a receiver analog front-end (AFE) (not shown in FIG.9.) Thus, the outputs of weighted buffers 935-937 may be based onincorrect decisions by samplers 925-927. However, the outputs ofsamplers 925-927 may be viewed as estimates of the current symbol andchoices for the weights of weighted buffers 935-937 selectedaccordingly.

FIG. 20 is a flowchart illustrating non-speculative DFE using an analogFFE. The steps illustrated in FIG. 20 may be performed by one or moreelements of communication system 100, memory system 200, and/orcommunication system 1200. A first sampler decision is produced bysampling a first analog output by an analog feed-forward equalizer thatreceives and equalized data signal (2002). For example, RxFFE 545 formedby S/H 540, weighted buffer 541, weighted buffer 542, and summer 511 maybe sampled by sampler 522 to produce a sampler decision.

A first error removal voltage is produced by weighting the first samplerdecision (2004). For example, weighted buffer 532 may weight the outputof tap logic 552, which is based on a subtraction of the samplerdecision from sampler 520, to produce an error removal voltage that isinput to summer 510.

A received data signal and the first error removal voltage are summed toproduce the equalized data signal (2006). For example, summer 510 maysum IN and the output of weighted buffer 532 to produce the input to S/H540 and weighted buffer 542.

FIG. 21 is a flowchart illustrating non-speculative DFE using acombination receive FFE and first tap DFE loop. The steps illustrated inFIG. 21 may be performed by one or more elements of communication system100, memory system 200, and/or communication system 1200. Using a firstDFE loop, a first sampler decision is produced based on a first errorremoval voltage and a weighted equalized data signal (2102). Forexample, sampler 620 may produce a sampler decision based on an errorremoval voltage from weighted buffer 642, where weighted buffer 642 ispart of a DFE loop formed by summer 611, sampler 620, and weightedbuffer 642.

The weighted equalized data signal is produced by weighting an equalizeddata signal (2104). For example, weighted buffer 641 may weight theequalized data signal output by summer 610. A second error removalvoltage is produced by weighting the first sampler decision (2106). Forexample, weighted buffer 632 may produce, based on the output of taplogic 652 which is based on a subtraction of sampler decision fromsampler 620, an error removal voltage that is input to summer 610.

An input data signal and the second error removal voltage are summed toproduce the equalized data signal (2108). For example, summer 610 mayreceive the output of weighted buffer 632 and sum it with the inputsignal IN to produce the input to weighted buffer 641.

FIG. 22 illustrates a communication system with an analog-to-digitalconverter (ADC) based receiver. Communication system 2200 comprises adriving integrated circuit, a receiving integrated circuit, andinterconnect between them. The driving integrated circuit includestransmitter circuit 2210 (a.k.a., a driver). The receiver integratedcircuit includes variable gain amplifier (VGA) 2251, continuous-timeequalizer (CTLE) 2252, analog-to-digital converter 2290, digital FFE+DFE2295, clock-data recovery 2291, phase adjuster 2293, and phase lockedloop 2292. The interconnect between the driving integrated circuit andthe receiving integrated circuit comprises interconnect system 2240.Interconnect system 2240 would typically comprise a printed circuit (PC)board, connector, cable, flex circuit, other substrate, and/or acombination of these. Interconnect system 2240 may be and/or include oneor more transmission lines.

The receiver integrated circuit would typically be part of an integratedcircuit that is receiving the signal sent by the driving integratedcircuit. It should be understood that termination (not shown in FIG. 22)can be part of the integrated circuit or interconnect system 2240. Itshould also be understood that although system 2200 is illustrated astransmitting a single-ended signal, the signals sent by the drivingintegrated circuit of system 2200 may represent one of a pair ofdifferential signals or one of a collection of signals sendingmulti-wire-coded data.

In FIG. 22, the output of transmitter circuit 2210 is connected to afirst end of interconnect system 2240. The second end of interconnectsystem 2240 is connected to the input of VGA 2251. The output of VGA2251 is input to CTLE 2252. The output of CTLE 2252 is input to ADC2290. The multi-bit and/or multi-sample digital outputs of ADC 2290 isinput to digital FFE+DFE 2295. Digital FFE+DFE 2295 is a multi-bitdecision OUT[1:N]. An output of Digital FFE+DFE 2295 is input to CDR2291. A recovered clock output by CDR 2291 is input to phase adjuster2293. Phase adjuster 2293 also receives a clock signal from PLL 2292.The output of phase adjuster 2293 is used to control the timing that ADC2290 samples the output of CTLE 2290. Transmitter circuit 2210 may beconfigured to drive PAM-4 signaling levels.

FIG. 23 illustrates a receiver with higher order DFE feedback in thedigital domain. Digital FFE+DFE 2300 illustrated in FIG. 23 maycorrespond to Digital FFE+DFE 2295. Digital FFE+DFE 2300 comprisesdigital summer 2310, FFE 2346, 1^(st) DFE tap 2347, weighted buffer2332, weighted buffer 2333, weighted buffer 2334, tap logic 2352, taplogic 2353, tap logic 2354, register 2362, register 2363, and register2364. FFE 2346 includes digital summer 2311, discrete-time derivative2371, and weighted buffer 2331. 1^(st) DFE tap 2347 includes samplerregister 2361 and weighted buffer 2332. In an embodiment Digital FFE+DFE2300 is configured to process samples of a PAM-4 signal and thereforereceives, via IN, a plurality of digital bits/samples (from, forexample, ADC 2290) and outputs a plurality of decision bits accordingly.In another embodiment, Digital FFE+DFE 2300 is configured to processsamples of a PAM-2 signal and therefore may output only a singledecision bit (e.g., OUT[1]).

A digital input signal (IN), which may be a plurality of bits and/or aplurality of samples, is operatively coupled to an input to summer 2310.The output of summer 2310 is input to FFE 2346. In particular, theoutput of summer 2310 is input to summer 2311 and discrete-timederivative 2371. In an embodiment, discrete-time derivative 2371implements a delay and subtraction such that discrete-time derivative2371 outputs according the equation: ffe_(out)=1−z⁻¹ where z⁻¹ is thevalue at the input to discrete-time derivative 2371 during the previousiteration (i.e., z⁻¹ represents the previous symbol input todiscrete-time derivative 2371. In an embodiment, K1=0.5α₁. Accordingly,it should be understood that K1 may be variable during an adaptation(i.e., training) period, but is typically constant during normaloperation.

The outputs of weighted buffer 2331, weighted buffer 2332, and summer2310 are input to digital summer 2311. The output of summer 2311 isinput to register 2361. The output of register 2361 is input to taplogic 2352 and weighted buffer 2332.

Discrete-time derivative 2371 and each of registers 2361-2364 receive atiming reference (not shown in FIG. 23.) Registers 2362-2364 eachserially receive the output of the previous register 2361-2264 therebyforming a serial shift register that, for each successive stage, holdsprevious values output by summer 2311.

The output of register 2361 is also input to tap logic 2352. Tap logic2352 subtracts the output of register 2362 from the output of register2361. The output of tap logic 2352 is input to weighted buffer 2332.Weighted buffer 2332 outputs the value at the input to weighted buffer2332 multiplied by the factor −K2. In an embodiment, K2=0.5α₂. Theoutput of weighted buffer 2332 is input to summer 2310 therebycompleting the second DFE tap loop. The output of register 2362 is alsoinput to tap logic 2353. Tap logic 2353 subtracts the output of register2363 from the output of register 2362. The output of tap logic 2353 isinput to weighted buffer 2333. Weighted buffer 2333 outputs value at theinput to weighted buffer 2333 multiplied by the factor −K3. In anembodiment, K3=0.5α₃. The output of weighted buffer 2333 is input tosummer 2310 thereby completing the third DFE tap loop. The output ofregister 2363 is also input to tap logic 2354. Tap logic 2354 subtractsthe output of register 2364 from the output of register 2363. The outputof tap logic 2354 is input to weighted buffer 2334. Weighted buffer 2334outputs the value at the input to weighted buffer 2334 multiplied by thefactor −K4. In an embodiment, K4=0.5α₄. The output of weighted buffer2334 is input to summer 2310 thereby completing the fourth DFE tap loop.Additional higher order DFE tap loops can be formed in a similar manner.

FIG. 24 is a flowchart illustrating a method of equalizing a datasignal. The steps illustrated in FIG. 24 may be performed by one or moreelements of communication system 100, memory system 200, and/orcommunication system 1200. A data signal is received (2402). Forexample, receiver 300 may receive an input data signal at node IN. Thisdata signal may be received by S/H 340 and weighted buffer 342 ofreceiver 300.

Based on a current symbol being received via the data signal, and aprevious symbol received via the data signal, an equalized data signalis generated (2404). For example, based on the current symbol beingreceived at node IN, and the output of S/H 340 (which corresponds to theprevious symbol that was received at node IN), summer 311 may output anequalized data signal to be sampled by PAM-4 sampler 320.

In an embodiment a circuit to receive a data signal and to output anequalized data signal includes a summer that receives the data signaland outputs the equalized data signal. The circuit also includes a firsterror signal generator to provide a first error removal signal to thesummer such that the equalized data signal is based on both the currentsymbol being received via the data signal and the previous symbol thatwas received via the data signal. The equalized data signal may be basedon a difference between the current symbol and the previous symbol. Thefirst error signal generator and the summer may be configured to form ananalog feed-forward equalization circuit. The first error signalgenerator and the summer may be configured to form an analoginter-symbol interference pre-filter and a first post-cursor decisionfeedback equalization loop. The first error signal generator and thesummer maybe configured to form an analog feed-forward equalizationcircuit and first post-cursor decision feedback equalization loop.

The circuit may also include a second error signal generator to providea second error removal signal to the summer such that the equalized datasignal is further based on a first prior symbol that is received via thedata signal prior to the current symbol, and a second prior symbol thatis received consecutively after the first prior symbol. The second errorsignal generator may be configured to base the second error removalsignal from the first prior symbol and the second prior symbol withoutusing combinational logic between a first storage element that storesthe first prior symbol and the summer. The data signal may be receivedby the summer in digital form and the first error signal generator andthe summer may be configured to form a discrete time digitalfeed-forward equalization circuit.

In an embodiment, a method of equalizing a data signal includesreceiving the data signal and, based on a current symbol being receivedvia the data signal and a previous symbol received via the data signal,generating an equalized data signal. The equalized data signal may bebased on a difference between the current symbol and the previoussymbol. The equalized data signal may be produced by an analogfeed-forward equalization circuit. The equalized data signal may beproduced by a circuit configured to form an analog inter-symbolinterference pre-filter and a first post-cursor decision feedbackequalization loop. The equalized data signal may be produced by acircuit configured to form an analog feed-forward equalization circuitand first post-cursor decision feedback equalization loop. The equalizeddata signal may be further based on a first prior symbol that isreceived via the data signal prior to the current symbol and a secondprior symbol that is received consecutively after the first priorsymbol.

The equalized data signal may be further based on the first prior symboland the second prior symbol without using combinational logic between asummer used to produce the equalized data signal and a plurality ofstorage elements that store at least the first prior symbol and thesecond prior symbol. The data signal may be received in digital form andthe equalized data signal may be produced in digital form by a discretetime digital feed-forward equalization circuit.

In an embodiment, a communication system includes a transmitter sendinga data signal having non-uniform pre-emphasis. This non-uniformpre-emphasis is applied to transitions from a first plurality of outputstates to a first output state. This non-uniform pre-emphasis is alsoapplied to transitions from a second plurality of output states to asecond output state. The non-uniform pre-emphasis is applied such thattransitions of the data signal from respective ones of the firstplurality of first output states are to be received, after traversing aband-limited channel, with substantially a first voltage level at areceiver sampling time. Likewise, the non-uniform pre-emphasis is alsoapplied such that transitions of the data signal from respective ones ofthe second plurality of output states are to be received, aftertraversing the band-limited channel, with substantially a second voltagelevel at the receiver sampling time. The communication system alsoincludes a receiver, to receive the data signal having non-uniformpre-emphasis after the data signal has traversed the band-limitedchannel. This receiver selects, based on a first comparator outputsampled at a previous receiver sampling time, between a first set ofcomparator outputs and a second set of comparator outputs. The selectedset of comparator outputs is to be used to determine an output of thereceiver corresponding to the receiver sampling time.

There may be three comparator outputs in each of the first set ofcomparator outputs and the second set of comparator outputs. The firstcomparator output may be based on a first reference voltage. A first oneof the selected set of comparator outputs may be based on the firstreference voltage. A second one of the selected set of comparatoroutputs may be based on a second reference voltage. A third one of theselected set of comparator outputs may be based on a third referencevoltage. The third reference voltage may be greater than the firstreference voltage. The second reference voltage may be less than thefirst reference voltage.

In an embodiment, a communication system, includes a transmitter sendinga data signal having non-uniform pre-emphasis. The non-uniformpre-emphasis is applied to transitions from a first output state, asecond output state, and a third output state to a fourth output state.The non-uniform pre-emphasis is applied such that transitions of thedata signal from at least the first output state and the second outputstate, to the fourth output state, are to be received, after traversinga band-limited channel, with substantially the same voltage level at thereceiver sampling time. The communication system also includes areceiver. The receiver is to receive the data signal having non-uniformpre-emphasis after the data signal has traversed the band-limitedchannel. The receiver is to use a first reference voltage to detect thefourth output state after transitions from the first output state andthe second output state to the fourth output state. The receiver is alsoto use a second reference voltage to detect the fourth output stateafter transitions from the third output state to the fourth outputstate.

The receiver may include a first sampler to produce a previous symbolsampler decision indicator based on a comparison of the data signalduring a previous symbol time to a first reference voltage. This firstsampler is to also produce a first sampler decision based on acomparison of the data signal during a current symbol time to the firstreference voltage. The receiver may also include a second sampler toproduce a second sampler decision based on a comparison of the datasignal to a second reference voltage during the current symbol time. Thereceive may also include a third sampler to produce a first samplerdecision based on a comparison of the data signal to a third referencevoltage during the current symbol time. The receiver may also include afourth sampler to produce a second sampler decision based on acomparison of the data signal to a fourth reference voltage during thecurrent symbol time. The receiver may also include a fifth sampler toproduce a second sampler decision based on a comparison of the datasignal to a fifth reference voltage during the current symbol time. Thereceiver may also include selection logic to, based on a first value ofthe previous symbol sampler decision indicator, use the second samplerdecision and the fourth sampler decision to produce output bits and alsoto be based on a second value of the previous symbol sampler decisionindicator, use the third sampler decision and the fifth sampler decisionto produce the output bits.

The third reference voltage may be greater than the second referencevoltage. The first reference voltage may be greater than the thirdreference voltage. The fourth reference voltage may be greater than thefirst reference voltage. The fifth reference voltage may be greater thanthe fourth reference voltage. The selection logic may comprise a firstmultiplexor to select between the second sampler decision and the thirdsampler decision and a second multiplexor to select between the fourthsampler decision and the fifth sampler decision. The output bits maycorrespond to four-level pulse amplitude modulation (PAM-4) signalinglevels. The non-uniform pre-emphasis may be applied to the transmitteddata signal such that transitions of the transmitted data signal from atleast a first output state and a second output state, to a third outputstate, are to be received, after traversing a band-limited channel, withsubstantially the same voltage levels at the receiver sampling time.

In an embodiment, a receiver circuit may include: a data signal inputthat is to receive a data signal transmitted with non-uniformpre-emphasis; a first sampler that is to produce a previous symbolsampler decision indicator based on a comparison of the data signalduring a previous symbol time to a first reference voltage, where thefirst sampler is to also produce a first sampler decision based on acomparison of the data signal during a current symbol time to the firstreference voltage; a second sampler that is to produce a second samplerdecision based on a comparison of the data signal to a second referencevoltage during the current symbol time; a third sampler that is toproduce a first sampler decision based on a comparison of the datasignal to a third reference voltage during the current symbol time; afourth sampler that is to produce a second sampler decision based on acomparison of the data signal to a fourth reference voltage during thecurrent symbol time; a fifth sampler that is to produce a second samplerdecision based on a comparison of the data signal to a fifth referencevoltage during the current symbol time; and, selection logic that is to,based on a first value of the previous symbol sampler decisionindicator, use the second sampler decision and the fourth samplerdecision to produce output bits. The selection logic to also, based on asecond value of the previous symbol sampler decision indicator, use thethird sampler decision and the fifth sampler decision to produce theoutput bits.

The third reference voltage may be greater than the second referencevoltage. The first reference voltage may be greater than the thirdreference voltage. The fourth reference voltage may be greater than thefirst reference voltage. The fifth reference voltage may be greater thanthe fourth reference voltage. The selection logic may include a firstmultiplexor to select between the second sampler decision and the thirdsampler decision, and a second multiplexor to select between the fourthsampler decision and the fifth sampler decision. The output bits maycorrespond to four-level pulse amplitude modulation (PAM-4) signalinglevels.

The non-uniform pre-emphasis may be applied to a transmitted data signalsuch that transitions of the transmitted data signal from at least afirst output state and a second output state, to a third output state,are to be received, after traversing a band-limited channel, withsubstantially the same voltage levels at the receiver sampling time. Thenon-uniform pre-emphasis may be applied by a transmitting integratedcircuit using a finite impulse response filter. The non-uniformpre-emphasis may be applied to four-level pulse amplitude modulation(PAM-4) signaling levels by the transmitting integrated circuit. Thereceiver circuit may be included in a memory device. The receivercircuit may be included in a memory controller.

In an embodiment, an integrated circuit may include an output to coupleto a band-limited channel; and, a transmitter to send a data signal viathe band-limited channel. The data signal to have non-uniformpre-emphasis. The non-uniform pre-emphasis to be applied to transitionsfrom a first output state, a second output state, and a third outputstate to a fourth output state. The non-uniform pre-emphasis to beapplied by the transmitter such that transitions of the data signal fromat least the first output state and the second output state, to thefourth output state, are to be received, after traversing theband-limited channel, with substantially the same voltage levels at thereceiver sampling time.

The data signal may be received by a receiving integrated circuit thatuses a first reference voltage to detect the fourth output state aftertransitions from the first output state and the second output state tothe fourth output state. The integrated circuit to also use a secondreference voltage to detect the fourth output state after transitionsfrom the third output state to the fourth output state.

The integrated circuit may further include a first sampler to produce aprevious symbol sampler decision indicator based on a comparison of thedata signal during a previous symbol time to a first reference voltage.The first sampler to also produce a first sampler decision based on acomparison of the data signal during a current symbol time to the firstreference voltage. The integrated circuit may further include a secondsampler to produce a second sampler decision based on a comparison ofthe data signal to a second reference voltage during the current symboltime. The integrated circuit may further include a third sampler toproduce a first sampler decision based on a comparison of the datasignal to a third reference voltage during the current symbol time. Thefourth sampler to produce a second sampler decision based on acomparison of the data signal to a fourth reference voltage during thecurrent symbol time. The integrated circuit may further include a fifthsampler to produce a second sampler decision based on a comparison ofthe data signal to a fifth reference voltage during the current symboltime. The integrated circuit may further include selection logic to,based on a first value of the previous symbol sampler decisionindicator, use the second sampler decision and the fourth samplerdecision to produce output bits, and to, based on a second value of theprevious symbol sampler decision indicator, use the third samplerdecision and the fifth sampler decision to produce the output bits.

The third reference voltage may be greater than the second referencevoltage. The first reference voltage may be greater than the thirdreference voltage. The fourth reference voltage may be greater than thefirst reference voltage. The fifth reference voltage may be greater thanthe fourth reference voltage. The receiving integrated circuit may be amemory device.

In an embodiment, a decision feedback equalizer, includes: a firstprevious symbol sampler to compare an equalized data signal to a firstreference voltage to produce a first previous symbol sampler decision; asecond previous symbol sampler to compare the equalized data signal to asecond reference voltage to produce a second previous symbol samplerdecision; a first current symbol sampler to compare a received datasignal to the first reference voltage to produce a first current symbolsampler decision; a second current symbol sampler to compare thereceived data signal to the second reference voltage to produce a secondcurrent symbol sampler decision; and, an analog summer circuit toreceive a first previous symbol error removal voltage that is based onthe first previous symbol sampler decision, and to receive a secondprevious symbol error removal voltage that is based on the secondprevious symbol sampler decision, and to receive a first current symbolerror removal voltage that is based on the first current symbol samplerdecision, and to receive a second current symbol error removal voltagethat is based on the second current symbol sampler decision, and toproduce the equalized data signal based on a delayed version of thereceived data signal, the first previous symbol error removal voltage,the second previous symbol error removal voltage, the first currentsymbol error removal voltage, and the second current symbol errorremoval voltage.

The first data sampler and the second data sampler may be part of aPAM-4 sampler. The first previous symbol error removal voltage, thesecond previous symbol error removal voltage, the first current symbolerror removal voltage, and the second current symbol error removalvoltage may have substantially equal magnitudes. The first previoussymbol sampler decision may determine a first sign of the first previoussymbol error removal voltage. The first current symbol sampler decisionmay determine a second sign of the first current symbol error removalvoltage. The first sign and the second sign may be opposite signs whenthe first previous symbol sampler decision and the first current symbolsampler decisions indicate the same result of respective comparisons tothe first reference voltage. The delayed version of the received datasignal may be produced by an analog sample and hold circuit thatreceives the received data signal.

The decision feedback equalizer may further include: a third previoussymbol sampler to compare the equalized data signal to a third referencevoltage to produce a third previous symbol sampler decision; a thirdcurrent symbol sampler to compare the received data signal to the thirdreference voltage to produce a third current symbol sampler decisionwhere the analog summer to further receive a third previous symbol errorremoval voltage that is based on the third previous symbol samplerdecision, and is to receive a third current symbol error removal voltagethat is based on the third current symbol sampler decision, and theequalized data signal is further based on the third previous symbolerror removal voltage and the third current symbol error removalvoltage.

The first previous symbol error removal voltage, the second previoussymbol error removal voltage, and the third previous symbol errorremoval voltage, the first current symbol error removal voltage, thesecond current symbol error removal voltage, and the third currentsymbol error removal voltage may have substantially equal magnitudes. Afirst difference between the first reference voltage and the secondreference voltage, and a second difference between the second referencevoltage and the third reference voltage may be approximately equal. Thefirst previous symbol error removal voltage and second previous symbolerror removal voltage may have substantially different magnitudesthereby effecting unique decision feedback weights for the firstprevious symbol sampler decision and the second previous samplerdecision. The first current symbol error removal voltage and secondcurrent symbol error removal voltage may have substantially differentmagnitudes thereby effecting unique decision feedback weights for thefirst current symbol sampler decision and the second current samplerdecision.

A method of receiving a data signal includes producing a first previoussymbol sampler decision indicator based on a comparison between anequalized data signal and a first reference voltage; producing a secondprevious symbol sampler decision indicator based on a comparison betweenthe equalized data signal and a second reference voltage; producing afirst current symbol sampler decision indicator based on a comparisonbetween a received data signal and the first reference voltage;producing a second current symbol sampler decision indicator based on acomparison between the received data signal and the second referencevoltage; based on the first previous symbol sampler decision indicator,producing a first previous symbol error removal voltage; based on thesecond previous symbol sampler decision indicator, producing a secondprevious symbol error removal voltage; based on the first current symbolsampler decision indicator, producing a second previous symbol errorremoval voltage; based on the second current symbol sampler decisionindicator, producing a second current symbol error removal voltage; and,summing at least a delayed version of a received data signal with thefirst previous symbol error removal voltage, the second previous symbolerror removal voltage, the first current symbol error removal voltage,the second current symbol error removal voltage to produce the equalizeddata signal.

The first previous symbol error removal voltage and the second previoussymbol error removal voltage may have substantially different magnitudesthereby effecting unique decision feedback weights for the firstprevious symbol sampler decision indicator and the second previoussymbol sampler decision indicator. The first previous symbol errorremoval voltage and the second previous symbol error removal voltage mayhave substantially different magnitudes than the first current symbolerror removal voltage and the second current symbol error removalvoltage.

The method may further include: producing a third previous symbolsampler decision indicator based on a comparison between the equalizeddata signal and a third reference voltage; producing a third currentsymbol sampler decision indicator based on a comparison between thereceived data signal and the third reference voltage; based on the thirdprevious symbol sampler decision indicator, producing a third previoussymbol error removal voltage; and, based on the third current symbolsampler decision indicator, producing a third current symbol errorremoval voltage; the third previous symbol error removal voltage and thethird current symbol error removal voltage summed with the delayedversion of the received data signal with the first previous symbol errorremoval voltage, the second previous symbol error removal voltage, thefirst current symbol error removal voltage, the second current errorremoval voltage to produce the equalized data signal.

A first difference between the first reference voltage and the secondreference voltage, and a second difference between the second referencevoltage and the third reference voltage may be substantially equal. Thefirst previous symbol error removal voltage, the second previous symbolerror removal, and the third previous symbol error removal voltage mayhave substantially unequal magnitudes thereby effecting unique decisionfeedback weights for the first previous symbol sampler decisionindicator, the second previous symbol sampler decision indicator, andthe third previous symbol sampler decision indicator. The first currentsymbol error removal voltage, the second current symbol error removal,and the third current symbol error removal voltage have substantiallyunequal magnitudes thereby effecting unique decision feedback weightsfor the first current symbol sampler decision indicator, the secondcurrent symbol sampler decision indicator, and the third current symbolsampler decision indicator. The method may also further includedelaying, by a symbol time, the received data signal to produce thedelayed version of the received data signal.

In an embodiment, an integrated circuit, includes: a first previoussymbol sampler to compare an equalized data signal to a first referencevoltage to produce a first previous symbol sampler decision; a secondprevious symbol sampler to compare the equalized data signal to a secondreference voltage to produce a second previous symbol sampler decision;a third previous symbol sampler to compare the equalized data signal toa second reference voltage to produce a second previous symbol samplerdecision; a first current symbol sampler to compare a received datasignal to the first reference voltage to produce a first current symbolsampler decision; a second current symbol sampler to compare thereceived data signal to the second reference voltage to produce a secondcurrent symbol sampler decision; a third current symbol sampler tocompare the received data signal to the second reference voltage toproduce a second current symbol sampler decision; an analog summercircuit to receive a first previous symbol error removal voltage that isbased on the first previous symbol sampler decision, and to receive asecond previous symbol error removal voltage that is based on the secondprevious symbol sampler decision, and to receive a third previous symbolerror removal voltage that is based on the third previous symbol samplerdecision, and to receive a first current symbol error removal voltagethat is based on the first current symbol sampler decision, and toreceive a second current symbol error removal voltage that is based onthe second current symbol sampler decision, and to receive a thirdcurrent symbol error removal voltage that is based on the third currentsymbol sampler decision, and to produce the equalized data signal basedon a delayed version of the received data signal, the first previoussymbol error removal voltage, the second previous symbol error removalvoltage, the third previous symbol error removal voltage, the firstcurrent symbol error removal voltage, the second current symbol errorremoval voltage, and the third current symbol error removal voltage. Thefirst previous symbol sampler, the second previous symbol sampler, andthe second previous symbol sampler may be configured as a PAM-4 sampler.

In an embodiment, a circuit to receive a data signal includes: a firstdata sampler to compare an equalized data signal to a first referencevoltage to produce a first sampler decision; a second data sampler tocompare the equalized data signal to a second reference voltage toproduce a second sampler decision; an analog summer circuit to receive afirst error removal voltage that is based on the first sampler decision,and to receive a second error removal voltage that is based on thesecond sampler decision, and to produce the equalized data signal basedon a received data signal, the first error removal voltage, and thesecond error removal voltage.

The first data sampler and the second data sampler may be part of aPAM-4 sampler. The first error removal voltage and the second errorremoval voltage may have substantially equal magnitudes. The firstsampler decision may determine a first sign of the first error removalvoltage and the second sampler decision may determine a second sign ofthe second error removal voltage.

The integrated circuit may further include: a third data sampler tocompare the equalized data signal to a third reference voltage toproduce a third sampler decision; and, the summer circuit to furtherreceive a third error removal voltage that is based on the third samplerdecision and to produce the equalized data signal based on the thirderror removal voltage. The first error removal voltage, the second errorremoval voltage, and the third error removal voltage may havesubstantially equal magnitudes. The first sampler decision, the secondsampler decision, and the third sampler decision may determine signs ofthe respective first error removal voltage, the second error removalvoltage, and the third error removal voltage. A first difference betweenthe first reference voltage and the second reference voltage, and asecond difference between the second reference voltage and the thirdreference voltage may be approximately equal.

In an embodiment a method of receiving a data signal includes: producinga first sampler decision indicator based on a comparison between anequalized data signal and a first reference voltage; producing a secondsampler decision indicator based on a comparison between the equalizeddata signal and a second reference voltage; based on the first samplerdecision indicator, producing a first error removal voltage; based onthe second sampler decision indicator, producing a second error removalvoltage; summing at least a received data signal with the first errorremoval voltage and the second error removal voltage to produce theequalized data signal.

The first error removal voltage and the second error removal voltage mayhave substantially different magnitudes thereby effecting uniquedecision feedback weights for the first sampler decision indicator andthe second sampler decision indicator. A first value of the firstsampler decision indicator may cause the first error removal voltage tocontribute to increasing the voltage of the received data signal toproduce the equalized data signal. A second value of the first samplerdecision indicator may cause the first error removal voltage tocontribute to decreasing the voltage of the received data signal toproduce the equalized data signal.

The method may further include: producing a third sampler decisionindicator based on a comparison between the equalized data signal and athird reference voltage; based on the third sampler decision indicator,producing a third error removal voltage; and, the third error removalvoltage summed with the received data signal, the first error removalvoltage, and the second error removal voltage to produce the equalizeddata signal.

A first difference between the first reference voltage and the secondreference voltage, and a second difference between the second referencevoltage and the third reference voltage may be substantially equal. Thefirst error removal voltage, the second error removal, and the thirderror removal voltage may have substantially unequal magnitudes therebyeffecting unique decision feedback weights for the first samplerdecision indicator, the second sampler decision indicator, and the thirdsampler decision indicator. The first decision indicator, the seconddecision indicator, and the third decision indicator may determinewhether a respective first error removal voltage, second error removalvoltage, and third error removal voltage respectively contribute toincreasing or decreasing the equalized data signal.

In an embodiment, an integrated circuit includes: a first data samplerto compare an equalized data signal to a first reference voltage toproduce a first sampler decision; a second data sampler to compare theequalized data signal to a second reference voltage to produce a secondsampler decision; a third data sampler to compare the equalized datasignal to a third reference voltage to produce a third sampler decision;an analog summer circuit to receive a first error removal voltage thatis based on the first sampler decision, and to receive a second errorremoval voltage that is based on the second sampler decision, and toreceive a third error removal voltage that is based on the third samplerdecision, and to produce the equalized data signal based on a receiveddata signal, the first error removal voltage, and the second errorremoval voltage.

The first error removal voltage, the second error removal voltage, andthe third error removal voltage may have substantially equal magnitudes.The first sampler decision, the second sampler decision, and the thirdsampler decision may determine signs of the respective first errorremoval voltage, the second error removal voltage, and the third errorremoval voltage. A first difference between the first reference voltageand the second reference voltage, and a second difference between thesecond reference voltage and the third reference voltage may beapproximately equal. The first data sampler and the second data samplermay comprise a PAM-4 sampler.

In an embodiment, a decision feedback equalizer (DFE) includes: ananalog feed-forward equalizer (FFE), the FFE to receive an equalizeddata signal and to produce a first analog tap output; a first sampler toreceive the first analog tap output and to produce a first samplerdecision; and, an analog summer to receive at least a received datasignal and a first error removal voltage that is based on the firstsampler decision, the summer to produce the equalized data signal.

The FFE may further include: an analog sample and hold to produce adelayed version of the equalized data signal; and, a summer to producethe first analog tap output, the summer to receive a current symbolerror removal voltage and a previous symbol error removal voltage, thecurrent symbol error removal voltage being based on the equalized datasignal, the previous symbol error removal voltage being based on thedelayed version of the equalized data signal.

The decision feedback equalizer may further include tap feedbackcircuitry to receive at least the first sampler decision and to producethe first error removal voltage. The tap feedback circuitry may receivea plurality of sampler decisions that includes the first samplerdecision, and produce a corresponding plurality of error removalvoltages corresponding to the plurality of sampler decisions, theplurality of sampler decisions corresponding to previous values of thefirst sampler decision.

In an embodiment, a method of receiving a data signal includes:producing a first sampler decision by sampling a first analog output byan analog feed-forward equalizer that receives an equalized data signal;producing a first error removal voltage by weighting the first samplerdecision; and, summing at least a received data signal and the firsterror removal voltage to produce the equalized data signal.

The method may also include: holding the equalized data signal toproduce a delayed analog version of the equalized data signal; weightingthe delayed analog version of the equalized data signal to produce aprevious symbol error removal voltage; weighting the equalized datasignal to produce a current symbol error removal voltage; and, producingthe first analog output by summing a current symbol error removalvoltage and a previous symbol error removal voltage.

The method may also include: weighting a second sampler decision toproduce a corresponding second error removal voltage that corresponds toa previous value of the first sampler decision where the second samplerdecision is summed with at least the received data signal and the firsterror removal voltage to produce the equalized data signal.

In an embodiment, a decision feedback equalizer (DFE) includes: a firsttap DFE loop that receives to receive an equalized data signal and toproduce a first sampler decision based on a previous symbol samplerdecision and the equalized data signal; and, a first analog summer toreceive at least a received data signal and a first error removalvoltage that is based on the first sampler decision, the summer toproduce the equalized data signal.

The first tap DFE loop may further include: first tap weightingcircuitry to receive the previous sampler decision and to produce afirst tap error removal voltage; equalized data signal weightingcircuitry to receive the equalized data signal and produce a weightedcurrent symbol voltage; a second analog summer to receive the weightedcurrent symbol voltage and the first tap error removal voltage; and, asampler to receive the output of the second analog summer and to producethe first sampler decision.

The decision feedback equalizer may further include tap feedbackcircuitry to receive a plurality of sampler decisions that include thefirst sampler decision, and produce a corresponding plurality of errorremoval voltages correspond to the plurality of sampler decisions. Theplurality of sampler decision may correspond to previous values of thefirst sampler decision.

The decision feedback equalizer may further include tap feedbackcircuitry to receive a plurality of sampler decisions that does notinclude the first sampler decision, and produce a correspondingplurality of error removal voltages correspond to the plurality ofsampler decisions. The plurality of sampler decision corresponding toprevious values of the first sampler decision.

In an embodiment, a decision feedback equalizer (DFE) includes: a firsttap DFE loop that receives to receive an equalized data signal and toproduce a first sampler decision based on a previous symbol samplerdecision and the equalized data signal; and, a first analog summer toreceive at least a received data signal and a first error removalvoltage that is based on the first sampler decision, the summer toproduce the equalized data signal.

The first tap DFE loop may further include: first tap weightingcircuitry to receive the previous sampler decision and to produce afirst tap error removal voltage; equalized data signal weightingcircuitry to receive the equalized data signal and produce a weightedcurrent symbol voltage; a second analog summer to receive the weightedcurrent symbol voltage and the first tap error removal voltage; and, asampler to receive the output of the second analog summer and to producethe first sampler decision.

The decision feedback equalizer may further include: tap feedbackcircuitry to receive a plurality of sampler decisions that include thefirst sampler decision, and produce a corresponding plurality of errorremoval voltages correspond to the plurality of sampler decisions, theplurality of sampler decision corresponding to previous values of thefirst sampler decision. The decision feedback may further include tapfeedback circuitry to receive a plurality of sampler decisions that doesnot include the first sampler decision, and produce a correspondingplurality of error removal voltages correspond to the plurality ofsampler decisions, the plurality of sampler decision corresponding toprevious values of the first sampler decision.

The systems and devices described above may be implemented in computersystems, integrated circuits, or stored by computer systems. The systemsdescribed above may also be stored on a non-transitory computer readablemedium. Devices, circuits, and systems described herein may beimplemented using computer-aided design tools available in the art, andembodied by computer-readable files containing software descriptions ofsuch circuits. This includes, but is not limited to, one or moreelements of system 100, system 200, receiver 300, receiver 302, receiver400, receiver 402, receiver 500, receiver 600, receiver 700, receiver800, receiver 900, receiver 1000, receiver 1100, system 1200, receiver1500, receiver 1600, receiver 1700, system 2200, digital FFE+DFE 2295,and their components. These software descriptions may be: behavioral,register transfer, logic component, transistor, and layoutgeometry-level descriptions. Moreover, the software descriptions may bestored on non-transitory storage media or communicated by carrier waves.

Data formats in which such descriptions may be implemented include, butare not limited to: formats supporting behavioral languages like C,formats supporting register transfer level (RTL) languages like Verilogand VHDL, formats supporting geometry description languages (such asGDSII, GDSIII, GDSIV, CIF, and MEBES), and other suitable formats andlanguages. Moreover, data transfers of such files on machine-readablemedia may be done electronically over the diverse media on the Internetor, for example, via email. Note that physical files may be implementedon machine-readable media such as: 4 mm magnetic tape, 8 mm magnetictape, 3½-inch floppy media, CDs, DVDs, Blu-Ray, and so on.

FIG. 25 illustrates a block diagram of a computer system. Computersystem 2500 includes communication interface 2520, processing system2530, storage system 2540, and user interface 2560. Processing system2530 is operatively coupled to storage system 2540. Storage system 2540stores software 2550 and data 2570. Computer system 2500 may include oneor more of system 100, system 200, receiver 300, receiver 302, receiver400, receiver 402, receiver 500, receiver 600, receiver 700, receiver800, receiver 900, receiver 1000, receiver 1100, system 1200, receiver1500, receiver 1600, receiver 1700, system 2200, digital FFE+DFE 2295,or components that implement the methods, circuits, and/or waveformsdescribed herein. Processing system 2530 is operatively coupled tocommunication interface 2520 and user interface 2560. Computer system2500 may comprise a programmed general-purpose computer. Computer system2500 may include a microprocessor. Computer system 2500 may compriseprogrammable or special purpose circuitry. Computer system 2500 may bedistributed among multiple devices, processors, storage, and/orinterfaces that together comprise elements 2520-2570.

Communication interface 2520 may comprise a network interface, modem,port, bus, link, transceiver, or other communication device.Communication interface 2520 may be distributed among multiplecommunication devices. Processing system 2530 may comprise amicroprocessor, microcontroller, logic circuit, or other processingdevice. Processing system 2530 may be distributed among multipleprocessing devices. User interface 2560 may comprise a keyboard, mouse,voice recognition interface, microphone and speakers, graphical display,touch screen, or other type of user interface device. User interface2560 may be distributed among multiple interface devices. Storage system2540 may comprise a disk, tape, integrated circuit, RAM, ROM, EEPROM,flash memory, network storage, server, or other memory function. Storagesystem 2540 may include computer readable medium. Storage system 2540may be distributed among multiple memory devices.

Processing system 2530 retrieves and executes software 2550 from storagesystem 2540. Processing system 2530 may retrieve and store data 2570.Processing system 2530 may also retrieve and store data viacommunication interface 2520. Processing system 2530 may create ormodify software 2550 or data 2570 to achieve a tangible result.Processing system 2530 may control communication interface 2520 or userinterface 2560 to achieve a tangible result. Processing system 2530 mayretrieve and execute remotely stored software via communicationinterface 2520.

Software 2550 and remotely stored software may comprise an operatingsystem, utilities, drivers, networking software, and other softwaretypically executed by a computer system. Software 2550 may comprise anapplication program, applet, firmware, or other form of machine-readableprocessing instructions typically executed by a computer system. Whenexecuted by processing system 2530, software 2550 or remotely storedsoftware may direct computer system 2500 to operate.

The foregoing description of the invention has been presented forpurposes of illustration and description. It is not intended to beexhaustive or to limit the invention to the precise form disclosed, andother modifications and variations may be possible in light of the aboveteachings. The embodiment was chosen and described in order to bestexplain the principles of the invention and its practical application tothereby enable others skilled in the art to best utilize the inventionin various embodiments and various modifications as are suited to theparticular use contemplated. It is intended that the appended claims beconstrued to include other alternative embodiments of the inventionexcept insofar as limited by the prior art.

1. (canceled)
 2. A receiver circuit comprising: an analog summer circuitto receive a first input signal and to produce an output data signalbased on a first error removal voltage and a second error removalvoltage; a first data sampler to sample a first sampler input signalbased on the output data signal using a first reference voltage toproduce a first sampler decision; and, a second data sampler to sample asecond sampler input signal based on the output data signal using asecond reference voltage to produce a second sampler decision, whereinthe first error removal voltage is generated from the first samplerdecision and the second error removal voltage is generated from thesecond sampler decision.
 3. The receiver circuit of claim 2, wherein thefirst sampler decision is multiplied by a first scaling factor togenerate the first error removal voltage.
 4. The receiver circuit ofclaim 2, wherein the second sampler decision is multiplied by a scalingfactor to generate the first error removal voltage.
 5. The receivercircuit of claim 2, wherein the first sampler decision is multiplied bya first scaling factor to generate the first error removal voltage, thesecond sampler decision is multiplied by a second scaling factor togenerate the first error removal voltage, and the first scaling factorand the second scaling factor have substantially equal magnitudes. 6.The receiver circuit of claim 2, wherein the first input signal isgenerated by applying decision feedback equalization to a second inputsignal.
 7. The receiver circuit of claim 6, wherein the decisionfeedback equalization applied to the second sampler input signal isbased on a third sampler decision produced by the first data sampler. 8.The receiver circuit of claim 6, wherein the decision feedbackequalization applied to the second sampler input signal is based on athird sampler decision produced by the second data sampler.
 9. Areceiver circuit, comprising: a first symbol sampler to compare a firstinput signal to a first reference voltage to produce a first symbolsampler decision; a second symbol sampler to compare the first inputsignal to a second reference voltage to produce a second symbol samplerdecision; and, an analog summer circuit to receive a first symbol errorremoval voltage that is based on the first symbol sampler decision, andto receive a second symbol error removal voltage that is based on thesecond symbol sampler decision, and to produce the first input signalbased on the first symbol error removal voltage, the second symbol errorremoval voltage, and a second input signal.
 10. The receiver circuit ofclaim 9, wherein the first symbol sampler decision is scaled by a firstscaling factor to produce the first symbol error removal voltage. 11.The receiver circuit of claim 9, wherein the second symbol samplerdecision is scaled by a first scaling factor to produce the secondsymbol error removal voltage.
 12. The receiver circuit of claim 11,wherein the second symbol sampler decision is scaled by a second scalingfactor to produce the second symbol error removal voltage, and the firstscaling factor and the second scaling factor to have substantially equalmagnitudes.
 13. The receiver circuit of claim 9, wherein the firstsymbol sampler decision determines a first sign of the first symbolerror removal voltage.
 14. The receiver circuit of claim 9, wherein thesecond input signal is an equalized version of a third input signal. 15.The receiver circuit of claim 14, wherein the third input signal isequalized based on a first previous decision by the first symbolsampler.
 16. The receiver circuit of claim 15, wherein the third inputsignal is equalized based further on a second previous decision by thesecond symbol sampler.
 17. A method of receiving a data signal,comprising: producing a first sampler decision based on a comparisonbetween a first input signal and a first reference voltage; producing asecond sampler decision based on a comparison between the first inputsignal and a second reference voltage based on the first samplerdecision, producing a first previous symbol error removal voltage; basedon the second sampler decision, producing a second previous symbol errorremoval voltage; and, summing the first input signal, the first previoussymbol error removal voltage, and the second previous symbol errorremoval voltage and to produce an output data signal.
 18. The method ofclaim 17, wherein the first sampler decision is scaled by a firstscaling factor to produce the first previous symbol error removalvoltage.
 19. The method of claim 17, wherein the second sampler decisionis scaled by a first scaling factor to produce the second previoussymbol error removal voltage.
 20. The method of claim 18, wherein thesecond sampler decision is scaled by a second scaling factor to producethe second previous symbol error removal voltage, and the first scalingfactor and the second scaling factor have substantially equalmagnitudes.
 21. The method of claim 18, further comprising: equalizing asecond input signal to produce the first input signal.